Those are two very different things.
ActivityPub is a protocol how messages etc. are travelling between servers that know how to use it. It has nothing to do with how someone can log in to your forum.
You can use oauth with a mastodon server. Which one of thousands servers you would use? Not mine, for sure. I mean there is not just one mastodon server, neither one login credentials. You can’t use (now anyway) any common Discourse login either.