Why would this cause a problem for Dorian?
It all depends on Dorian's general behavior as a magister, his outlook on the position, and how much the Tevnter standard of appearance plays into any of that and the role it may have in him accomplishing his goals.
We know Dorian doesn't want to hide who he is, or loves, but he may think that playing along with expectations will enable him to do a better job. But again, it depends on how he is going to be going about doing that job. If he's of the mind that anyone who would be concerned about such things is a throwback whose alliance is not worth cultivating, then there isn't a problem. But if he is looking ahead and thinking, rightly so, that the way to do it is to bring the old guard to your side, make them see that change is needed, that will be more easily done if he's not viewed as too much of an upstart.
He considered himself a pariah before, for his sexuality and his views regarding that and the rest of Tevinter society. But he is not the same person he was five years ago, when the only thing he had to worry about was himself and his own personal torments. He's helped saved the world and he wants to save his country, issues much larger than his own desires.
But this is all conjecture. We don't know exactly how the Inquisitor (the person -- for our purposes in this thread, the man) is viewed by the rest of the altus class, or the Magisterium at large. We don't know how many people are aware of the romantic relationship between Dorian and the Inquisitor (aside from the one banter with Vivienne), what they think of that, and if it's just assumed that it is quid pro quo pleasure and power based and nothing of true significance (why would they think otherwise?) You have to remember, having such a romantic attachment would be seen as a weakness and something to exploit, regardless of who it's with.
Also, just because the Inquisition has formally disbanded (for some players), doesn't mean that there won't be those, including possibly the Archon, who may see the Inquisitor's presence as a threat; they weren't fans of the Inquisition to begin with.