To be clear I am not advocating this - it can all feed into the same BGS.
On a really, really basic level it could be something like CZs in Open that don't appear in PG/Solo, and drives a competition between two factions, and likewise PG/Solo only have a BGS activity for a similar pair of warring factions.
Very simple example using no new content, but you get what I mean. It's additional pieces of content for either, not splitting affairs in any way. I do believe splitting the BGS would be "ideal" in my eyes, but I acknowledge it will never happen and ultimately is not right for this game.
Pretty sure the 'Open only' content in the past was available to all players regardless of modes. All that the devs can do is verify that the player did not play in one of the other modes to move the gameplay forward.
Because, there are no modes. The devs cannot limit something to only those that choose to see everyone...because the game does not work in that manner!
The content HAS to be in all the modes...and cannot be prevented from scoring in any 'mode' a player chooses. The only way that a players activity can be verified is to have a dev look at each account and see that the player never logged in with a different 'desire to see people'.