Ok, revising my conditions here. Looking for a compromise.
If I can play the single player game without ever being aware that it has a link to the multiplayer, I will be happy. As in, if there are no in game indicators like the one in the War Room in ME3 that constantly remind you that there's something in the multiplayer you should be doing. Having the multiplayer option on the title screen is fine. I can tune that out. Also, if there is not obviously something missing such that it leads me to investigate and discover that that thing can only be gotten through multiplayer. This includes:
1) Items/locations/whatever that are mentioned in single player dialog before you unlock them in the multiplayer (mentioning them after they're unlocked is fine)
1a) This includes things like items being listed in shops with some special icon to indicate they haven't been unlocked yet.
2) A key mechanic/ strategic asset/character/ thing affecting the end game that won't go above a certain level such that its obvious, leading me to discover that it can only be obtained/sufficiently boosted through multiplayer.
So if you want to reward multiplayers with unique but non essential items for the single player, thats fine. If you want to reward multiplayer grinding in a way that reduces the need for single player grinding, thats fine (as long as I can still get whatever it is through single player grinding). EDIT: Actually, that would be kind of neat. Something like a "Skip Fetch Quest" token or even a "Skip Towers of Hanoi" token. I guess the drawback being that it might tempt the devs to really pack in the fetch quests and towers of hanoi.
I don't want another Levi Dryden and I don't want a perpetual 50% anywhere in the game. I don't want an advisor hanging out in my keep reminding me that I've neglected the [Insert BS Multiplayer mechanic]. Or anything like that.