To answer the questions asked above:
Do you remove your hat during the National Anthem? YES
If you were at a game with friends and they didn't remove their hat would you instruct them to do so? YES
If you were at a game and saw a stranger that had their hat on, would you ask them to remove it? YES
If you were at a game and saw a stranger that had their hat on, would you tell them to remove it? YES, if they didn't do it when I asked them to.
If they still refuse, it will be removed for them.
To sum things up:
Removing your hat during the National Anthem is mandatory.
Anyone who thinks otherwise, was not raised properly.