Disagree. The culture in which those kids are raised in reinforces/normalizes such thought and behavior in school and elsewhere. They're not going to be embarrassed by their parents unless perhaps they're living in a mostly liberal region.
But that's exactly the effect we have seen over the past several generations.
I doubt that homophobia will drop anymore than racism has in the red states
Racism has dropped dramatically. I hope to see homophobia do the same.