So here's something I used to wonder about which may bear dusting off now that we know Cullen's a LI. Given how duty-bound he is, I always imagine him having very strong opinions about chain of command. So, now imagine Cullen is the Inquisitor's subordinate and he reports to her. Or say, he's not technically under her (no pun intended, hurr hur hurr), so it's not really fraternization, but she still outranks him. How would this impact a romance? How would he feel about it? How would your Inquisitor feel about that?
Well, depending on the circumstances, Cullen might still view himself as part of the templars. Thus, having a relationship with the Inquisitor, who is not part of the Chantry and is powerful enough to protect themselves, could be seen as a positive. If Cullen feels he's part of the Inquisition, that means he's probably left the templars for some reason, and he might no longer feel beholden to their rules and regulations.
Or perhaps Cullen remembers his inappropriate crush on Amell/Surana and is especially sensitive to rankings and power structure. He might be wary about not his own rank in relation to the Inquisitors, but, rather, how his own subordinates will see him, if he's an NPC, or how the other companions will react, if he's a follower.
My own Inquisitor will have different views based on who they are. Ashtal will have no problem, Kushem will find it amusing, Cookie... dunno, she's my first-at-bat. A human mage might be uncomfortable with their own feelings for him.