There's a slight difference there though. TOS Klingons are supposed to be friendly to Klingon aligned, same faction and all that. And they are, except they show up under the enemy filter setting, which they shouldn't.
That's a bug. They aren't enemies, they shouldn't show up in that setting.
What you are talking about is an additional feature or content. The ability to have your own faction be the enemy. And, yes, that is something we need, especially Klingon side, with the history of House violence.
Having 2 groups of each, one ally, one enemy, would be a bit of a hack fix. You'd need it for all the Klingon aligned races, for example. And even then, it wouldn't address all issues. My story, for example, puts the player in the middle of a conflict between two houses. So I need Klingons who are the enemies of Klingons, with the player able to shoot both. So I'd need 2 enemy faction Klingon groups. And suppose you wanted a story with Hirogen fighting Romulans. Guess what, those two factions won't fight each other. And there's no doubt other examples. The end result would be a rather cluttered list.
For that situation, we need a better way to be able to set hostility. Say the ability to set whether a group sees the player as enemy, ally, or neutral (and hooks to let us change that as the mission progresses), as well as to set other groups as being the enemy, either by a list of groups or else some sort of faction we can set for a group and the ability to give that group or faction enemy groups/factions.
A bit more work involved there for the devs to properly fix it.
Be glad you don't have races with their own fleets, a history of fighting your own faction, and that there's a Terran Empire
