I think the question I might have is, let's say the new Trek series is set a few years after Enterprise. Let's say there's interest in guest appearances from that cast, or even having actors from previous series' guest-star in new roles (as Rene Auberjonois did on Enterprise).
Would involvement in Axanar sour CBS on Gary Graham or JG Hertzler because of their involvement with Axanar? I think a lot of it will have to do with how the actors react to the whole situation. If they claim ignorance and are apologetic, maybe no harm. But if they "ally" themselves with Axanar, defend it publicly, then perhaps it gives CBS pause.
If somehow Axanar comes away with any kind of win (where the produce any kind of version of Axanar) and someone like Graham continues in his role (as another similar character, but not Soval) CBS might still be hesitant to cast him in any new role, perhaps just out of principle.
As for their broader careers? Not sure it will have much effect.