I wear glasses and they’ve never moved on any Disney ride. You should be good. Be aware that Splash and Kali will muck up your glasses. You’re probably going to need a little dry towel to wipe them off after any water ride.
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Most of the rides at Disney don’t require you to take your glasses off. The only exception in my experience, as a life-long glasses wearer, is Space Mountain. I forgot to take my brand new multi-focals (i.e., very expensive) off and when we went down the first dip they flew off my face and I caught them mid-air. It was luck that I actually caught them because it was dark and I couldn’t see. Anyway, moral of the story, I’d take my glasses off for Space Mountain. 
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I got a three pack of straps for pretty cheap off Amazon, just in case. I’m not too worried about me, but DD would be miserable without her glasses and DW without her sunglasses.
I also wear a strong glasses prescription but didn’t have a problem at Philharmagic. It might be very individual based on the prescription of the wearer.