Nobody is saying it actually happened as far as i've seen. Its a what if situation
Whether he is known around spokane as a predator is irrelevant. If he hasn't actually done anything in the shelter there is no reason for them to do anything, until and unless he does. He could have been to prison for murder but as long as he doesn't try to kill anybody while he is there they wouldn't make an issue of it. Now that would change very quickly if he actually tried to kill someone, same as if he tried to sexually assault someone. That said, I find it very unlikely people aren't going to notice somebody trying to sexually assault a teen girl in any manner. That tends to lead said teen girls to lose their shit and cause a scene which is quite likely to be noticed. Aside from that, I think you may be vastly overestimating how well known lucas actually is, even in spokane. The city is the state epicenter for nutjobs just like him. Aside from the starbuck incident, which is likely either largely forgotten or was never that well known publicly to begin with, he hasn't really done that much to draw attention to himself specifically. Not stuff that the average person is going to be aware of at any rate.
That aside, there are plenty of limitations to the examples you gave. They can be high or drunk when they get there without being turned out, provided they don't start shit or anything of that nature, but the shelter can't allow them to, or look the other way on actually allowing someone to get high or drunk while in the building. They'd get nailed legally for facilitating it if anything happened afterwards, there or if they were allowed to leave. So yeah, they allow alot of questionable people in, but there are tighter restrictions than may be immediately apparent, to protect their own asses