Yes, I know that he reveals his secret ID in Civil War. But since that doesn't really make much sense (since no one knows who he is so it's weird anyone would care), why not just have him straight-up reject to reveal his secret ID and never reveal it in the movie?
He just shows up prior or after the Registration Act, and adamantly rejects the notion. Cap takes the role of Spider-Man (i.e. initially supports the Act, but then rejects it) and Spidey is running the underground resistance from the start.
This would be a twist to the story (so it's not a straight rehash), plus it let's Marvel make Spider-Man anyone (well, except for women). Is it Peter Parker? Is it Miles Morales? You could even cast both of the characters as minor supporting characters to feed speculation. It'd be a nice mystery and to my mind would be a nice way of transcending the racial issue, by letting Spider-Man not be defined by a race or ethnic group.