It fits perfectly without a screen protector. Apparently it won’t close entirely (but it will be close) if you use a thick screen protector, but I’m having trouble finding out what exact extra thickness is OK. It seems like very thin film based protectors are within tolerance.
As long as it’s only film, not glass screen protector you should be fine.
People use screen protector for various reasons. Some are paranoid to accidental scratch (when detached from keyboard), or better drawing (for paper-like type).