I personally love the ambiguous nature of it all myself. I'm asexual, and I find it rather interesting that I managed to romance a character where it can be interpreted as one if you so wish. I'm curious to why it's such a big deal though? As Sylvia said, it's fully up to you.
The sweetness is too much though. I had to get a filling from it all.
It's kind of cool to hear about this. I relate to asexuality pretty strongly, and it's cool to hear about Josephine's romance. I'm still only in the Hinterlands, Storm Coast, and Fallow Mire, though, LOL. I just found this thread through Google because I was searching up Josephine Montilyet and she's really adorable and shiny and gorgeous and ugh♥ I'm fairly smitten. Then again, I pretty much love all of the characters! It's crazy! Blackwall interests me, Cullen interests me, Iron Bull interests me, Josephine interests me....and I NEED to romance Solas as an elven inquisitor on my next playthrough!!! And Cassandra on another. My cousin would like me to be with Sera, though--she's shipping us hardcore. Anyway, um, yeah. Josephine is powerful and super cute and ahh
So yeah, I don't see a problem with the percieved lack of physical display of affection, it's kinda nice that there are different presentations of a romance in the game, honestly.
It's part of the game's (and life's) charm!