What? This is ridiculous. Hold their help hostage? Blackmail? Why do you think they are obligated to help someone? I'm really sorry you're going through a hard time OP, and I really hope you get back on your feet soon. I have been there. Homeless and hiding while pregnant with 2 small kids. Perhaps had I been alone I would have had room for your level of indignance, but I had to think of my kids. So I stayed with my aunt and uncle. In exchange for their silence about my presence I went to church, I went to bible study, I cleaned their house every day, I cooked them dinner, and I humbly did everything they asked of me until I could find a better option.
Most Christians aren't terrible people. They believe they have something special to show you that will change your life for the better. They are wrong, but they genuinely want to share with you. In exchange for hearing them out they're offering you a safe place to stay and probably food. If you refuse that offer that is your choice, but you have no right to say you're homeless because you're atheist. It sounds more like homeless because you're too proud to take the help that is offered to you.
Most Christians aren't terrible people. They believe they have something special to show you that will change your life for the better. They are wrong, but they genuinely want to share with you. In exchange for hearing them out they're offering you a safe place to stay and probably food. If you refuse that offer that is your choice, but you have no right to say you're homeless because you're atheist. It sounds more like homeless because you're too proud to take the help that is offered to you.