I came out to my friend yesterday, and ever since I've been feeling this discomfort between us whenever we're talking. He has told me that (since he's religious) he doesn't support the gay lifestyle, but he won't judge me and he never wants me to feel uncomfortable, and that he wants us to talk about our problems with each other and he doesn't want this to come between us. While I know what he's saying is truthful, there is still this feeling of discomfort between us. Should I leave it alone and give him space, or do I bring my thoughts to his attention and see how he feels about the situation?
In my experience, anytime you come out to someone there is a period of awkwardness. I'd just let it go if I were you.
I just came out to a Christian friend. I told him "I know you believe that homosexuality is immoral and while I disagree, I respect your view. I hope that you will also respect mine." He said he does, and that he has more respect for me now than he did before I told him, and that he expects our friendship to become deeper because of it. Like SomeNights said, it's pretty common for people to experience some awkardness after coming out to a religious friend, or anyone for that matter. However, it might be helpful to clarify that you respect your friend's beliefs even though they differ from yours, and that he doesn't need to change his beliefs in order to be your friend and to support you.
Being religious doesn't have to equate to being homophobic, and I think that's what your friend is trying to do. It's difficult to question your faith at times. And you know he may one day realise that maybe whether you are gay or not means nothing to him. It will go away sooner or later if you continue to talk to him and hang out. I think what your friend is trying to do is very admirable, despite being religious he's not resorting to bigoted slander. And whatever his religion is, he's doing one thing that any God in their right mind wants, to love and accept. Good Luck