First time I have ever had issues with a screen protector while using a case is with my HTC 10 and Diztronic case. I finally ordered a new case (Incipio for $6 on Amazon) and this one I can tell will be no problem at all with my screen protector. It definitely leaves a little more room around the edges than my old case which would push up the edge of the screen protector. I wonder how the Spigen compares.

I do still mostly blame my screen protector which is the ArmorSuit for not properly cutting their "case friendly" version. Actually started with the regular version and the case friendly version was no better. It cuts down the top and bottom a little but that wasn't the problem. It is the width. But then again I'd never had any issue with any other phone/case/screen protector combo and never had to but case friendly versions before, so it may very well be a poorly designed case.

Haven't used tempered glass screen protectors in awhile so have no recommendation, but I can say the Incipio + ArmorSuit definitely works and the ArmorSuit screen protector is very good aside from the case friendly version maybe being slightly too wide. With the Incipio case being so cheap it may be worth a try to see if it is more screen protector friendly than Spigen. Only have had the case for 24 hours but seems like it is made very well.

Edit: Didn't realize there were multiple Incipio cases for HTC 10. I bought this one: https://www.amazon.com/Incipio-Carrying-Case-HTC-Packaging/dp/B01EAQ6BIE