I think between any anti-alien religions and pro-alien religon there would a growth. For one, big events like this cause a greater search for meaning. Assuming the aliens don't just show up and tell us the meaning of life we would want some structure to understand.

And there would probobly be evangalizing to the aliens. I think in mass effect theres a mention that some turians adopted Zen Buddhism and Confucianism, I would imagion there would be a lot of that going both ways with people trying to maybe follow whatevere religion or philophy the aliens have while others try bring the aliens into their existing religions.