I actually like to play more Multiplayer games than I do. More in the direction of "co-op". I do play a lot of Multiplayer games but one is Dota 2, which none of my friends want to play with me anymore (I'm a terrible person) and the other is Mabinogi, which none of my friends wants to play with me anymore (have I mentioned that I'm a terrible person?). well, in terms of mabinogi it's more of "We are not interested in it currently/anymore". Bah, and when it finally got new interesting stuff, can't beat that new dungeon alone.
Anyway, I like to team up with someone and, considering what types of games I play, most of the time I like to plan ahead with them, discuss about the game etc. As you mentioned, there are people that want to do their thing and don't like to play the game another way. had these moments too, many of them, these types of Steam friends didn't last long honestly. I'm the same as you in that term, I don't like to pushed in one direction. Ironically I can be really pushy in many cases. The friends I have now, that soemtimes still play with me (really rarely) however are more of the "Just do the planning and we follow" stuff, so, I have to do all the planning myself mostly. I'm a little straneg in that regard, I want others to contribute to plannign but I also want it to have my own ideas in it. Which soemtimes does not work in specific games.
I stopped playing Dungeon Defenders 2 multiplayer, because evry time you go there, there is always that one guy who builds everything himself and if you try to add your own stuff, he will quickly spam the chat or ping you to remove it and also demand to hand him all your building mana. In that regard, DD2 is really toxic and it kind of ruined the game for me. Sanctum is more open minded about this.
I also like story about video games. A lot. I know there are some people here (calling out Misery again) that don't like stories at all in video games and just want the game for the game(play). I like to have both in games but I also liek to have games, that focus more on the story as on the actual gameplay. But I also don't want them to have only story, as Visual Novels for an example, because I could just read a book that way. Text based adventures are sometimes okay, like Sorcery, which is almost entirely story but features so many different decision paths, that you will barely notice that you just read a book.
The problem with friends, in terms of story is, spoilers. This is the one thing I hate the most. It doesn't even have to be somethign about the story, even stuff like important late gameplay elements cpuld go on my nerves. I rage on this stuff, when someones shows me somethign I didn't know before and wanted to find out myself. Screenshots are the worst in that regard, it's a literal picture that shows me what will happen int he game. There is a spoiler option for a reason!
Ugh!
So in that regard I have to be careful, what my friends play. Som of them don't even think about it, when they post this stuff.