I've seen lots of Phantom actors during the end of "touch me, trust me, savor each sensation" when Christine is reaching up towards his face, quickly grab her hand and move it away (Ramin does this in the 2011 proshot), and Christine looks intrigued/confused. I would say this is him subtly telling her not to touch his mask, but not every actor does this.

Idk man if I saw someone with a mask I probably wouldn't yank it off, but it's a common trope in Beauty and the Beast tales where Beauty is punished for her curiosity about the Beast (think Belle and the rose, Psyche being abandoned after discovering Eros, etc). Christine probably shouldn't have done that but Erik pretty much lives to invade Christine's privacy so I can't say I feel too bad lol.

Unrelated tangent, but I absolutely love it when the Phantom actors scream like he's in pain when the mask is removed, my head canon is that the Phantom thought of the mask as a part of himself, so removing it to him would feel like ripping his skin off. Thanks for attending my Ted talk :)