Alternatively, couldn't they just make it a requirement for co-op that all players have to have the mission unlocked individually in order to play it? That way you can't be pulled forward but can still play together.
This is likely why the full campaign is replayable with a fireteam after you've cleared it the first time. After you've beaten it once they can ensure everyone has access to what they need to have access to, so it doesn't matter anymore.
I'm gonna repost this for a new page since a lot of people seem to be missing it and I think it explains this decision:
This single player set of story missions is the key to unlocking all of the different regions in the solar system.
This is what it says in the guide, and with the narrative focus on regaining what you've lost the odds are that the campaign is structured in such a way that people playing together would be a technical issue if they had out of sync story progression. For example, if you complete Homecoming and I've already cleared the campaign and you invite me to your fireteam, I could then select for us to travel to a planet which is out of sync with your story progression. Or maybe I have access to my Super or a subclass that you still need to earn via the campaign missions. Destiny 1 works like that in the first few missions. You have to unlock the preliminary features like interplanetary travel before co-op opens up. Like I said above, that's probably why it's do-able as a fireteam AFTER you've already beaten the campaign once. Because that ensures that players have synced up progression and so they can get away with it.
I'm just saying that this explains the decision, rather than people thinking they're getting screwed just because. Whether or not you agree with progression being that deeply ingrained into the storyline is a separate discussion, but I like to think understanding
why you can't have access to a feature helps you come to terms with it. You'll get co-op story missions, just clear them once so you can unlock the basic features and full scope of locales in Destiny 2 first.