I suppose, generally, but I go to a state university, you do need to swipe your active student ID card to enter the library through a turnstile. I've also attended many hackathons at other unis where turnstiles exist as well and you can't enter unless you're a student there.

I mostly remember because of the pain it was to get clearance from security at those unis to be able to get out of the hackathon (at their libraries) and get back in; had to leave ID and take my visitor badge with me.

I'm sure many state unis are open to residents of that state, but I know not all. To be honest, I prefer it to be that way for the same reason "actual" public libraries just aren't conducive for actually studying something that takes a lot concentration.