"Anyone could be under that mask" meaning Peter Parker is an everyman, not that there should be two-spirit gay spidermans or whatever dumb shit they're pushing.

Everyman means if you're black or hispanic or whatever white Peter Parker represents you as well, as opposed to say superman who's power is innate as one of the (((Chosen People))); to imagine yourself as a black superman you have to imagine yourself as a white Kryptonian.

What makes these particular race swaps dumb is that what makes him spiderman is the unique circumstances of his origin story. Uncle Ben dying because of Peter's own selfishness, being charged "with great power comes great responsibility" by that uncle - these are what makes him spiderman. Any other person bit by a radioactive spider would be defined by that selfishness, or vanity, or religion, or whatever else was in their own unique back story.

So if you retell the story with black Uncle Ben Ben's Originals that's fine, but if you retell it with random dude from alternate universe that just doesn't work - without the origin story they're an entirely different character.