i preordered the uag monarch for the note 8 and i think they are screen protector friendly.
atleast for the s8+ they said so on amazon and also alot of youtube videos proofed this. so i think it will be the same for the note 8.
it all depends on how case friendly the protectors really are.
for example the whitestone dome should work fine with uag cases. no test yet for the note 8 but they did on the s8+