I'd say, rather, that the approximate events of Superman: The Movie and Superman II are part of its continuity, but that doesn't mean it's reciprocally part of the continuity of the Christopher Reeve movie series -- which overtly took place 20-odd years earlier (sorry, the "timeless" thing doesn't cut it since it was presented as very much a contemporary piece) and included three movies (counting Supergirl) that SR doesn't acknowledge. They're two separate continuities that have two movies' worth of events approximately in common -- much like every Superman continuity shares events like the destruction of Krypton and Kal-El being found by the Kents. (Or like how there are seven distinct Godzilla film continuities that all include the 1954 film but otherwise contradict each other massively.)
That's the thing about fictional continuity -- since it's all made up anyway, one work can claim another as being in its continuity (at least after a fashion) but that doesn't mean the reverse will be true. Look at all the cases where an animated TV series spinoff presented itself as a direct sequel to a movie, only to be ignored by the movie's own sequels (e.g. The Real Ghostbusters, Men in Black, the MTV Spider-Man, etc.). Two things can be in continuity and out of continuity with each other at the same time.
After all, the continuity of fictional works is as imaginary as everything else about them. It's not an objectively real thing, it's just another storytelling device like everything else, and that makes it just as mutable and subject to the whims of storytellers.
Which was also used by the 1988 Superman animated series. And Danny Elfman's Batman theme has been used in at least four different continuities -- the Burton movies, B:TAS, the Justice League feature, and now here in the Earth-99 scenes.
I would also prefer a naked cameo by Henry Cavill. Doesn't mean it's going to happen. Have you got a problem with that?
