FWIW, though I see you've already started writing, I think it's not only okay, it's something I like for its own sake. By which I don't just mean that I like to do it. Rather, I like to read fics that used to be (and are no longer) consistent with canon! First, because sometimes I decide I don't like canon at a certain point. Second, because it forms a sort of record of what fandom was thinking at the time the fic was started. Third, because I love the idea of two creators following the same prompt or drawing from the same sketch; seeing multiple different fans (and the canon creator!) take on the challenge of continuing a series from a specific point is fun!

I have no idea what fandom you're talking about, but if it's one I'm in, I'm glad you're writing it!