I have been to my library yes. You don't need ID or a library card (unless you want to check something out or use a computer) and you can pick up any book you like (including e.g. 50 Shades of Grey), sit down at a table, and read it. There are children in there all the time and there isn't an adults-only section.
If your goal is "prevent children from accessing adult material", it really isn't that limited.
> underaged kids can not checkout non kid material without adult in the loop
They don't need to. They can read it in the library; that's what libraries are for.