Every Florida library I've been in requires a library card. If you don't live in the county that the library is in, they don't issue you a card. You have to show your drivers license to get a card. The county that address is in, is where your card can be used and computer time can be scheduled (usually in 30 min to 1 hour increments). A few times when I've moved, I showed my house closing papers or rental agreement if my drivers license had not been updated yet.
Now for the college libraries, you have to be a staff member or student. You can walk in and visit but you cannot use a computer or check out any materials.