I always use a screen protector. And on the XS I'm using one that covers the notch, and I have no problems at all.
I never go without, as the oleophobic coating on every screen wears of after about 3 months. And then it's finger-smudge city. With no screen protector, your screwed. With screen protector, you just put on a new one, and everything clean and smudge free again.
Been using screen protectors on my iPhone since 4S. No case. On the XS Max I went full screen that covers notch area. To me look betters and no issues what so ever. Face ID works fine and proximity as well. On previous X went full screen as well.
I have been trying different screen protectors and my most recent one is a full coverage privacy glass one. No difference with FaceID between having a cutout and not, if anything it seemed to help as I can now unlock my phone at impressive off-angles.