I *do* like the idea of having a sweet, uncomplicated, "traditional" romance, with a female character, but the way it's implemented, yeah, I wish they could have done *something* to show that Josephine likes women. Even once the romance has started, I've been trying to find out if there's any dialogue that shows how her family feels about her romancing a woman...I mean, it doesn't have to be disapproval, maybe they're accepting, that would be nice to show too. Does the man dueling the Inquisitor for Josephine's hand react differently if it's a female character? That seems like an obvious place to put different dialogue based on gender.
As far as I know there is no difference with the duel. I'm conflicted about that.
On the one hand, I love that I got to be all romantic & dashing which may not have happened if the romance was different for female Inquisitors. On the other hand, it would be nice if there were some differences.
I mean Joesphine is the head of her family, I at the very least expected a conversation about who would carry on her family name if she didn't have children. I know she has siblings, but the oldest having kids can be important in lines of succession so I'd liked a reference to that.
They proved my point yet again that the main straight female romance is always the most important to the plot. Sera being the lesbian only, she isn't that important and can get kicked out anytime. This pisses me off so much, you don't even know. We finally get a lesbian in DA and they go and make her "temporary". Ugh!
And don't tell me the lame excuse that "she can be annoying". Everyone can be annoying, i personally didn't find her annoying at all. Others would've loved to kick Viv out or even Blackwall (though you can do if you do his personal quest but still not like Sera where the option is right there always)
I see the same formula over and over again and i'm getting tired of this tbh. I'd like for once to see a "main" lesbian romance who can never get kicked out AND is important to the plot. 
I feel like Sera is the only one you can kick out at will, everyone else seems to only leave if their approval goes low enough or at a certain point in their personal quest.
I would love for a lesbian romance that is important to the plot & who can't leave.
In fact I'd prefer if more romances felt tied more to the plot. In DA:O Morrigan & Alistair's seemed to interact more with the overall plot, in DA:I, out of 8 possible LIs Cassandra's seems to be the only one that is tied to the plot.
Please correct me if I'm wrong though I've only romanced Josephine so far & I haven't finished yet, so this is an assumption based on the importance of Cassandra's personal quest is to the plot of DA:I.