I wouldn't let strangers stay in my home. For starters, it's a health and safety nightmare (it's a small house, so I have stuff like a weight bench, squat rack and free weights + dumbells in the kitchen where someone could trip over them then, knowing my luck, be able to sue for it).
Secondly, I work from home and have a lot of expensive stuff that I wouldn't feel comfortable leaving in the house while a stranger was there.
I did once let a stranger stay in my home (I bumped in to him while walking home with my husband during some extreme and unexpected snowstorms, and when we heard how far he had to walk we figured it was the decent thing to do). He was a model guest, and we're still in touch today, but it felt odd having a stranger in the house.