I got rift S as my first headset, so I don't have much to compare it to, except that I tried a Vive for 5 minutes at a store one day. In each case I tried with my glasses first.
(in my case I don't totally need my glasses. Eyes are good enough that I pass the driving test without them, but I use them for better reading of computer screens and such. Subtle prescription)
In my case I have large-ish plastic frames. Not crazy big, but far from small. The headset does push on the glasses and it's a little hard on my nose, but they do fit in Rift S. My understanding is that Rift S has more room than previous Rift models. (but I don't have personal experience with them)
I ultimately decided that I prefer to play with my glasses off since I can get the lenses closer to my eyes and it feels like the overall image (sweet spot, vs edge) is more even. In other words: with my glasses the sweet spot is slightly sharper, but the edges are more blurry and my FoV is narrower since the HMD is farther from my eyes. If I really needed my glasses to see the image I could do it. I think I would be looking at options like insert lenses (though I'm very skeptical of those) or more likely, an aftermarket facial gasket like those from VR Cover. I'm still watching for those to come out since the foam on the Rift S is very cheap and not great. Something from VR cover might improve the glasses user experience quite a bit.
TL : DR
Yes, glasses fit unless they are really huge; though you'll probably be farther from the lenses so the FoV is narrower. Like slightly more scooba effect.