Can, say, Mary Jane show up in Civil War or not?

You mean characters that affect Peter's life personally? Like Aunt May?

If so, yes.

@krspacet: Well, we don't know the exact details of the deal yet.

For instance, only Spider-Man/Peter Parker might be able to appear in the main MCU movies (Civil War, Infinity War etc.) but the rest of his supporting cast will most definitely appear in the Marvel/Sony produced movies.

An interesting question to ask would be, could characters like Ned Leeds and Jean DeWolff appear both in the Spider-Man movies and in the Daredevil Netflix series. It'd make sense considering DD and Spidey's worlds interconnect almost perfectly in the comic books, but Sony may not allow it (God knows why).