The mosques and gurdwaras in my nearest town were the first vaccine hubs. And the religious leaders have stepped up right from the beginning, encouraging their congregations to get the vaccine.
So I don't think religion blaming is the way to go for anyone. The BAME issue with vaccines goes deeper than that, and is historical. When your cultural history is of being experimented on by medics and scientists, as your life was worth less than whites, you don't grow up trusting those such things.
OP was clearly just stirring with her post.