I visited the "gate" at the border to Cyrodiil....but entry was denied. So guess I need to "join" my alliance in order to get entry?
You have to choose an alliance at character creation time. There is no requirement to ever fight other players, though. And no requirement to ever join your faction's army in Cyrodiil. That is completely optional. And you always get to explore all 3 factions' story/quest lines no matter what. You start with your own, then move to another faction, then when you finish that, you can move on to the 3rd faction.