"If I get in contact with someone who wants to room with me or rent my home, and I find out that they are not a Christian as they previously posted online, do I have grounds to turn them down?"
Yes! In order for them to post their profile online, they had to agree 100 Percent with the Apostles' Creed. Because they contacted you via this website, they were making a public statement to you that they were officially a Christian.
If they told you any lie, even one such as that one, when communicating with you on the issue of business, those could be grounds to mistrust them regarding other issues. And that, my friends, is definitely grounds for terminating a business-related application, whether it's for employment or rent.
Bear in mind that the nature of disagreements caused by trying to mix a Christian with an pre-Christian in such a close setting would in itself be enough cause to terminate that roommate relationship. And since most people on this site who say they are a "Landlord" do qualify as a roommate (meaning, they still live in the house), then they would have even more justification for denying a roommate relationship.
Disclaimer: Talk with your attorney about this, blah, blah, blah...