I am sure that if you had personal experiences to go on then you would see that it is a majority. In Seattle only one such "church" has done something which doesn't push it's beliefs onto those who need their services, all others however (save when they aren't allowed to because of federal/state funding) have. I lived "in the system" for almost 7 years before I finally got out, thanks to the one organization. I wear a pentacle, proud to be a pagan (not the ones you see on TV but it's purist definition), got turned away by all others because of it, one made the request that I take off the pentacle. But the one that actually helped made no stipulations, they simply said "here" ... and here's a list of resources you may find helpful in getting more help (all state run). Compass Center,
Compass Center :: Welcome
We have five organizations in Seattle that are "church" run, only one does not require some form of conversion or for you to participate, that's one in five. Other states I have been to the number holds, Indiana was the worst, Colorado was a little better, but on average it's one in five that actually just "help". Another is the type of help, Compass does more than just hand you what you need, they also encourage you to get schooling, jobs, etc. and hook you up with those resources, while the others require you to become part of their religious practices but will only give you basic needs.