I moved out of SF during the pandemic but before that the city had homeless and mentally ill people and there was no security check at the library, and it was full of books.
https://sfist.com/2013/08/27/were_doomed_sf_main_library_bat...
And yes, with children access to a bathroom is necessary.
Also now elsewhere and going to library is so fun. We can bike etc. they are reasonably strict though. No sex, drugs, sleeping etc
I contrast that with the library in Austin. Obviously, as a free, warm, comfortable space, there are tons of homeless people there. But, unlike in SF, the Austin library doesn't let them trash the place - the homeless there are just using the library like everyone else. There is a strict no sleeping/lying rule (which I've seen enforced) which prevents anyone from basically taking over a section of the library. The bathrooms have always been immaculate whenever I've used them.
IMO the Austin library's policy toward the homeless shows how you can be respectful and welcoming to all while still requiring everyone who enters to respect the building.