While I love the idea of faction music in general, I never found a game that implemented it in a way that I found satisfying. What I mean in the case of Starsector is that your interactions with a "faction" screen is most of the time extremely short. For example:
You could fly near a station with the ambiance music, get pinged,
have the com dialog warning you about the inspection with the Hegemony theme,
get back to space waiting for the fleet to catch up with the ambiance music back,
then have the Hegemony neutral music again for a second while accepting the inspection,
get back to the ambiance music for 5 seconds during the inspection progress,
get the second inspection screen with the Hegemony music for 5 seconds,
get back to space/ambiance,
dock to the station/Hegemony theme, sell your food and
get back to space 5 seconds later with the ambiance... (and optionally get pinged again ><)
That's eight switches between the beginning two musics intro in probably less than 30 seconds. (I also really dislike how in the current implementation the musics start from the beginning for each market interaction)
All in all once you start to play a bit faster the music would be all over the place, and this is one of the most common succession of screens you'll get in the game. What could help against that is having a "faction" ambiance music fading in when approaching a market while still in space. Then the dialog screen only add emphasis on an already present theme, and since most of your interactions near a market are with that market factions the changes would be less jarring. Of course that's just my opinion...