I don't see why they can be part of the main universe. Agent Carter does have issues with Captain America going back in time but I guess that raises the old question of whether or not he created alternate timeline. I think he did and likely was very active at stopping or trying to stop lots of the bad things that he knew could happen, from knowing they happened in the main universe. I kind of like the idea that this new universe is were the Mutants were created and who will eventually merge into the main universe.
I don't know about that. Let's pretend that Chris Evans going back in time does not create an extra timeline. If he doesn't meet up with Peggy until after the events of her series and keeps a low profile in the shadows then it sheds a different light on the Winter Soldier scene but doesn't really contradict it. We could also assume that the Inhumans in SHIELD moved to the Moon or something shortly after Season 3 as there is nothing in the movies that directly contradicts their existence up until that point. SHIELD is still in the mainstream MCU up until the Season 5 finale. The only thing contradicting Season 6 being in the MCU universe is the idea that it is highly unlikely that all the members of the team survived the blip.