At my undergrad school, which was pretty open for physical access pre-COVID (who knows what happens now), I'd need to pay for a borrowing card to actually check out a book. And electronic access seems to have been tightened up. You used to be able to access most of their electronic catalog from a public terminal on the local network but you couldn't seem to do that last time I tried maybe about 18 months ago. (It wasn't a big deal so I didn't feel like bothering a librarian.)

And some universities will definitely require ID to enter the library.