If it were my doorstep? First, I'd be surprised because I live out in the country. Then I would be finding out what these folks need and get it for them, if possible. Be it food, shelter, medical help, money.....opportunities to help people should never, ever be turned down, IMO.
If they pooped on my porch, I would let them use my bathroom! Heck, the cat throws up on my porch every other day....big ol' piles of rabbit hair. The dogs poop in my yard and so do the chickens, sheep and cow. Actually, the cow piles a big steamy right in front of my back door at least once a week.
Dirty? Let them use my bathroom. Cold? Give them warm clothes and the offer of a warm bed. I'd offer to wash their clothing. I'd offer to take them where they want to go.
Yes, I know some of these people may be dangerous, some may be out for the chance to steal something. I don't fear these things. I don't need to because God is my Shepherd and I fear no evil. End of story.
A church should never fear doing the right thing. No matter how inconvenient, no matter how messy....doing the right thing is always the right thing.