That non-enrolled people can access, of course.
In the US, universities are required to provide information on the web about required textbooks to students so that they can purchase the books from wherever they want without necessarily having to buy the textbooks from the college bookstore.
A search on Google using the name of the university and "required textbooks" will typically take you to a website that has this data. You will probably need to cross-reference this information with the course catalog to know what courses are taken in what order within the academic program you're interested in.
In some cases, instructors will use materials that they've developed themselves and that students access through a course management system. In that case, it's quite likely that the materials won't be visible to you.
Is there a university website that lists all books used/recommended per course in order?
Mostly yes. At American universities you can visit the website of the campus bookstore. This is usually a private company (not the university itself) which has gathered a list of required textbooks (not necessarily all books used) from faculty. The bookstore will be happy to tell you what books you can buy for each course, even if you are are not a student. A major limitation is that the websites usually only list recent courses. If the course was not offered for a while, the information might have been deleted.