“For Jesus Himself testified that a prophet has no honor in his own country. So when He came to Galilee, the Galileans received Him, having seen all the things He did in Jerusalem at the feast; for they also had gone to the feast.” John 4:44-45 NKJV
There were indeed many in Galilee who believed in Jesus.
The point made in multiple Gospel accounts is that the people around whom Jesus grew up struggled to see Him as more than just the carpenter's son.
From Luke 4:
14 And Jesus returned in the power of the Spirit into Galilee: and there went out a fame of him through all the region round about.
15 And he taught in their synagogues, being glorified of all.
16 And he came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day, and stood up for to read.
Luke then proceeds to record Jesus' teaching and the reaction of the people present, including:
22 And all bare him witness, and wondered at the gracious words which proceeded out of his mouth. And they said, Is not this Joseph’s son?
(note that the community thought Jesus was Joseph's son)
Mighty as Jesus was in word and deed, many could not get over the fact that someone they had known as a child could be anyone significant. Most people from other Galilean communities didn't know Jesus as a child and so wouldn't have this struggle.
This is a very insightful observation about human nature--we're often willing to see strangers as great and wonderful people--but those we know up close we tend not to grant the benefit of the doubt.
Let us be clear about what Jesus did say in Matt 4:44 -
For Jesus Himself testified that a prophet has no honor in the own hometown (= Nazareth). [See also Luke 4:24]
Jesus then was received positively in Cana - quite separate from Nazareth where he was rejected (Luke 4:28-30).
Jesus was also received positively in Capernaum (Luke 4:23), again, quote separate from Nazareth but still in the region of Galilee.
Those closest to Jesus, who grew up with him, had the most trouble respecting him.
After this Jesus went about in Galilee. He would not go about in Judea, because the Jews were seeking to kill him. 2 Now the Jews’ Feast of Booths was at hand. 3 So his brothers said to him, “Leave here and go to Judea, that your disciples also may see the works you are doing. 4 For no one works in secret if he seeks to be known openly. If you do these things, show yourself to the world.” 5 For not even his brothers believed in him. 6 Jesus said to them, “My time has not yet come, but your time is always here. 7 The world cannot hate you, but it hates me because I testify about it that its works are evil. 8 You go up to the feast. I am not going up to this feast, for my time has not yet fully come.” 9 After saying this, he remained in Galilee. (John 7:1–9, ESV)
It was the same where he grew up in Nazareth.
They said, “Is not this Jesus, the son of Joseph, whose father and mother we know? How does he now say, ‘I have come down from heaven’?” (John 6:42, ESV)
In wasn't until his death and resurrection that his brothers decided to believe Jesus.
But motioning to them with his hand to be silent, he [Peter] described to them how the Lord had brought him out of the prison. And he said, “Tell these things to James [Jesus' brother] and to the brothers.” Then he departed and went to another place. (Acts 12:17, ESV)
James, the apostle, the brother of John, had been executed (Acts 12:1).
There is also a difference between welcoming someone and honoring them as a prophet. Just because his brothers didn't believe him doesn't mean they wouldn't welcome him.