Hm. As I plan to play a Qunari Inquisitor, who does actually like and support the Qun, being Bros with anyone may not be his Thing. However, I can see him get along very well with the more serious, "no nonsense" Characters like Cullen (I'm actually pretty sure about them getting along) and Blackwall (he strikes me as such, at least). Cassandra and Vivienne (the latter one with a big Question Mark) may also qualify, but I expect... ideological Differences with them. He will also actively seek out Iron Bull to be teached about the Qun, as it is known that a Qunari Inquisitor will start out as a Vashoth, and a Ben Hassrath isn't the worst Person to introduce one to the Qun.
However, I can't see him being on friendly Terms with Varric. Ever. Those two will butt Heads, that's for sure. I expect the same Problems with Dorian, him being Tevintri and all. Sera might fare better, but the ideological Differences I can see arising with Cassandra and Vivienne will be even more poignant with her. Solas is too unknown to be judged that Way, but I can see Problems arising from that Direction. Leliana is the same - assumed she has at least partially retained her kind Heart and deep Faith, this may cause Conflict.
Scribbles and Cole are the least known Variables. The Former doesn't even have a Name and i know the Latter only from his Wiki Article, but I am cautiously optimistic in that Direction.