Luke 3:6 And ALL flesh shall see the salvation of God.
DOGS are not referring to Gentiles in general.
Mar 7:26 The woman was a Greek, a Syrophenician by nation; and she besought him that he would cast forth the devil out of her daughter.
Mar 7:27 But Jesus said unto her, Let the children first be filled: for it is not meet to take the children's bread, and to cast it unto the dogs.
Mar 7:28 And she answered and said unto him, Yes, Lord: yet the dogs under the table eat of the children's crumbs.
There were precedent cases that Gentiles have been granted eternal life with Lord Jesus even though not rulers with the 12 tribes of Israel.
Greek has also been promised Salvation.
Act 11:4 But (Apostle) Peter began and explained it to them in order: (Act 11:5-14)
Act 11:15 As I (Peter) began to speak, the Holy Spirit fell on them just as on us at the beginning.
Act 11:16 And I remembered the word of the Lord, how he said, 'John baptized with water, but you will be baptized with the Holy Spirit.'
Act 11:17 If then God gave the same gift to them as he gave to us when we believed in the Lord Jesus Christ, who was I that I could stand in God's way?"
Act 11:18 When they heard these things they fell silent. And they glorified God, saying, "Then to the Gentiles also God has granted repentance that leads to life."
Rom 15:15 But on some points I (Paul) have written to you very boldly by way of reminder, because of the grace given me by God
Rom 15:16 to be a minister of Christ Jesus to the GENTILES in the priestly service of the gospel of God, so that the offering of the Gentiles may be acceptable, sanctified by the Holy Spirit.
Rom 15:17 In Christ Jesus, then, I have reason to be proud of my work for God.
Rom 15:8 For I (Paul) tell you that Christ became a servant to the circumcised (Jew) to show God's truthfulness, in order to confirm the promises given to the patriarchs,
Rom 15:9 and in order that the Gentiles (non-Jew) might glorify God for his mercy. As it is written, "Therefore I will praise you among the Gentiles, and sing to your name."
Rom 15:10 And again it is said, "Rejoice, O Gentiles, with his people."
Rom 15:11 And again, "Praise the Lord, all you Gentiles, and let all the peoples extol him."
Rom 15:12 And again Isaiah says, "The root of Jesse will come, even he (Jesus) who arises to rule the Gentiles; in him will the Gentiles hope."
Rev 22:12 (Jesus said) And, behold, I come quickly; and my reward is with me, to give every man according as his work shall be.
Rev 22:13 I am Alpha and Omega, the beginning and the end, the first and the last. "
Rev 22:14 Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city.
Witness 2 (Apostle Matthew)
Mat 1:21 And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their SINS.
Mat 26:27 And he (Jesus) took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it;
Mat 26:28 For this is my blood of the new testament, which is shed for many for the remission of SINS.
Sura 3:55 Behold! God said: "O Jesus! I will take thee and raise thee to Myself and clear thee (of the falsehoods) of those who blaspheme; I will make those who follow thee (Jesus) SUPERIOR to those who reject faith, to the Day of Resurrection: ... (Yusuf Ali Translation)
Faith in Jesus is superior than disbelievers.
There are several cases that Lord Jesus was not sent only to the Jews but to the whole human race. Lord Jesus was not a racist as some disbelievers like to discredit him.
The salvation has not come to the Gentiles until the event at Caesarea. It was Apostle Peter who witnessed that the Holy Spirit was also given to Cornelius a centurion of what was known as the Italian Cohort (Gentile) and his household at Caesarea.
Act 10:34 So Peter opened his mouth and said: "Truly I understand that God shows no partiality,
Act 10:35 but in every nation anyone who fears him and does what is right is acceptable to him.
Act 10:36 As for the word that he sent to Israel, preaching good news of peace through Jesus Christ (he is Lord of all),
Act 10:37 you yourselves know what happened throughout all Judea, beginning from Galilee after the baptism that John proclaimed:
Act 10:38 how God anointed Jesus of Nazareth with the Holy Spirit and with power. He went about doing good and healing all who were oppressed by the devil, for God was with him.
Act 10:39 And we are witnesses of all that he did both in the country of the Jews and in Jerusalem. They put him to death by hanging him on a tree,
Act 10:40 but God raised him on the third day and made him to appear,
Act 10:41 not to all the people but to us who had been chosen by God as witnesses, who ate and drank with him after he rose from the dead.
Act 10:42 And he commanded us to preach to the people and to testify that he is the one appointed by God to be judge of the living and the dead.
Act 10:43 To him all the prophets bear witness that everyone who believes in him receives forgiveness of sins through his name."
Act 10:44 While Peter was still saying these things, the Holy Spirit fell on all who heard the word.
Act 10:45 And the believers from among the circumcised who had come with Peter were amazed, because the gift of the Holy Spirit was poured out even on the Gentiles.
Act 10:46 For they were hearing them speaking in tongues and extolling God. Then Peter declared,
Act 10:47 "Can anyone withhold water for baptizing these people, who have received the Holy Spirit just as we have?"
Act 10:48 And he commanded them to be baptized in the name of Jesus Christ. Then they asked him to remain for some days.
Act 11:18 When they heard these things they fell silent. And they glorified God, saying, "Then to the Gentiles also God has GRANTED repentance that leads to life."
In another event, Samaritan leper was also healed by Jesus. Samaritan are people of mixed blood between Jews and Gentiles in Samaria and they were considered unclean by the Jews. Basically, Samaritan are Gentiles by Jewish standard.
Luk 17:12 And as he entered a village, he was met by ten lepers, who stood at a distance
Luk 17:13 and lifted up their voices, saying, "Jesus, Master, have mercy on us."
Luk 17:14 When he saw them he said to them, "Go and show yourselves to the priests." And as they went they were cleansed.
Luk 17:15 Then one of them, when he saw that he was healed, turned back, praising God with a loud voice;
Luk 17:16 and he fell on his face at Jesus' feet, giving him thanks. Now he was a Samaritan.
Luk 17:17 Then Jesus answered, "Were not ten cleansed? Where are the nine?
Luk 17:18 Was no one found to return and give praise to God except this foreigner?"
One read that Jesus also clensed a Gentile or foreigner but did not deny the request of the leper. So will Jesus deny the salvation of the Gentiles?
Another evidence that Lord Jesus did not deny the salvation of Gentiles, is from the event he met a Samaritan woman at Jacob's well.
Joh 4:5 Then cometh he (Jesus) to a city of Samaria, which is called Sychar, near to the parcel of ground that Jacob gave to his son Joseph.
Joh 4:6 Now Jacob's well was there. Jesus therefore, being wearied with his journey, sat thus on the well: and it was about the sixth hour.
Joh 4:7 There cometh a woman of Samaria to draw water: Jesus saith unto her, Give me to drink.
Joh 4:8 (For his disciples were gone away unto the city to buy meat.)
Joh 4:9 Then saith the woman of Samaria unto him, How is it that thou, being a Jew, askest drink of me, which am a woman of Samaria? for the Jews have no dealings with the Samaritans.
Joh 4:10 Jesus answered and said unto her, If thou knewest the gift of God, and who it is that saith to thee, Give me to drink; thou wouldest have asked of him, and he would have given thee living water.
Joh 4:11 The woman saith unto him, Sir, thou hast nothing to draw with, and the well is deep: from whence then hast thou that living water?
Joh 4:12 Art thou greater than our father Jacob, which gave us the well, and drank thereof himself, and his children, and his cattle?
Joh 4:13 Jesus answered and said unto her, Whosoever drinketh of this water shall thirst again:
Joh 4:14 But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life.
Joh 4:15 The woman saith unto him, Sir, give me this water, that I thirst not, neither come hither to draw.
Joh 4:16 Jesus saith unto her, Go, call thy husband, and come hither.
Joh 4:17 The woman answered and said, I have no husband. Jesus said unto her, Thou hast well said, I have no husband:
Joh 4:18 For thou hast had five husbands; and he whom thou now hast is not thy husband: in that saidst thou truly.
Joh 4:19 The woman saith unto him, Sir, I perceive that thou art a prophet.
Joh 4:20 Our fathers worshiped in this mountain; and ye say, that in Jerusalem is the place where men ought to worship.
Joh 4:21 Jesus saith unto her, Woman, believe me, the hour cometh, when ye shall neither in this mountain, nor yet at Jerusalem, worship the Father.
Joh 4:22 Ye worship ye know not what: we know what we worship: for salvation is of the Jews.
Joh 4:23 But the hour cometh, and now is, when the true worshipers shall worship the Father in spirit and in truth: for the Father seeketh such to worship him.
Joh 4:24 God is a Spirit: and they that worship him must worship him in spirit and in truth.
Joh 4:25 The woman saith unto him, I know that Messiah cometh, which is called Christ: when he is come, he will tell us all things.
Joh 4:26 Jesus saith unto her, I that speak unto thee am he.
Joh 4:27 And upon this came his disciples, and marveled that he talked with the woman: yet no man said, What seekest thou? or, Why talkest thou with her?
Joh 4:28 The woman then left her waterpot, and went her way into the city, and saith to the men,
Joh 4:29 Come, see a man, which told me all things that ever I did: is not this the Christ?
Joh 4:30 Then they went out of the city, and came unto him.
Joh 4:31 In the mean while his disciples prayed him, saying, Master, eat.
Joh 4:32 But he said unto them, I have meat to eat that ye know not of.
Joh 4:33 Therefore said the disciples one to another, Hath any man brought him aught to eat?
Joh 4:34 Jesus saith unto them, My meat is to do the will of him that sent me, and to finish his work.
Joh 4:35 Say not ye, There are yet four months, and then cometh harvest? behold, I say unto you, Lift up your eyes, and look on the fields; for they are white already to harvest.
Joh 4:36 And he that reapeth receiveth wages, and gathereth fruit unto life eternal: that both he that soweth and he that reapeth may rejoice together.
Joh 4:37 And herein is that saying true, One soweth, and another reapeth.
Joh 4:38 I sent you to reap that whereon ye bestowed no labor: other men labored, and ye are entered into their labors.
Joh 4:39 And many of the Samaritans of that city believed on him for the saying of the woman, which testified, He told me all that ever I did.
Joh 4:40 So when the Samaritans were come unto him, they besought him that he would tarry with them: and he abode there two days.
Joh 4:41 And many more believed because of his own word;
Joh 4:42 And said unto the woman, Now we believe, not because of thy saying: for we have heard him ourselves, and know that this is indeed the Christ, the Savior of the world.
An eunuch from Ethiopia also came to accept Jesus as the Son of God and was baptized. So the Gentiles are in the salvation plan of God.
Act 8:27 And he (Philip) arose and went: and, behold, a man of Ethiopia, an eunuch of great authority under Candace queen of the Ethiopians, who had the charge of all her treasure, and had come to Jerusalem for to worship
Act 8:35 Then Philip opened his mouth, and began at the same Scripture, and preached unto him Jesus.
Act 8:36 And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?
Act 8:37 And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
Salvation is for all!