Yes, there is a very slight difference in armor between male and female, but this is completely different model (brown hooded Jedi robe vs a blueish puffy jacket)
I think I've found out what is going on - the armor does convert to Imperial version. Confirmed on another piece called "Polyfibe Chestguard"
1. How it looks in my character's eq and a picture from net displaying how it looks in game (also on my Kira while not in cutscenes): https://imgur.com/a/xGtCHXG
2. How it looks when equipped by Kira and picture from net displaying how it looks in cutscenes: https://imgur.com/a/3f3Y3M7; you can even see my Kira in the background wearing proper model, while the icon displays a black Imperial suit, which shows up in cutscenes.
According to torf.mmo-fashion.com (I know, not particularly legit, but it's not like we've got a database with all models), it's the same armor but in different Rep/Imp variants.
Also I went a bit overboard saying all cutscenes - it's ship cutscenes + few more (see spoiler); both direct companion quests and Jedi Knight story quests.
Not gamebreaking, just a bit annoying; still, a bug is a bug.
Thanks, that makes sense; there's still a few issues with new forums - I was only able to create this thread via Incognito mode, although I guess good ol' cookie cleaning should do the trick.