I use a stylus only because I don't like the fingerprints. Never used a screen protector on my Ipads or Iphones. No reason for them.
Depending on the screen protector, most of them are very prone to scratches. I get more scratches on my screen protector than I usually do without it. Must be because I buy terrible ones.
The iPad's screen is very scratch resistant. Only the high end glass style screen protectors are as hard, or harder.
On the other hand, most screen protectors are cheap, so replacing them once or twice a year is no big deal.
Personally, I've never had a significant problem with scratches on my iPad, or my iPhone. And I keep the iPhone in a pocket. But that can vary not only based on personal habits but on where you live. Some places are just grittier than others.
Like really sharp finger nails.....
You can scratch your iPad screen with your fingernails? Who are you, Chuck Noris?
Not the screen, the screen protector, if grown long enough.