Short of racism, the only "story reason" for her to be gated against non-humans would likely involve her being of noble birth, which can be twisted around just as easily to justify her being gated against humans as well.
So there are logical reasons for Cassandra to be unromanceable by the Inquisitor that is most similar to her, both culturally and in his background, but to be race-gated against non-humans comes down to nothing more than racism or her being of noble birth? Gotta disagree there. Everything we've seen of Cassandra so far has indicated that her noble ancestry means very little, if anything, to her. I can't see it being a barrier to any of the races, human or no.
And there are plenty of logical reasons for her to be race-gated against non-humans that have nothing to do with shallow racism, or even indirect racism. But these are non-racist reasons why I think Cassandra could be race-gated if the devs decided she should be:
Qunari - I doubt Cassandra has a high opinion of mercenaries. To her, that could be a profession in which you are selling your own soul for a little bit of coin. You have no beliefs of your own, and nothing that you are fighting for other than worldly goods. I think she could find that distasteful.
Dwarf - Coterie connections and criminal past. Just like the Qunari's mercenary occupation, this could serve as a serious barrier. Who knows what kind of things a Coterie dwarf has done to survive? Plus, the lyrium smuggling has led to serious problems within the Circle and the Templar Orders. She could associate the dwarf Inquisitor with the corruption leading up to the Mage-Templar war.
Dalish - The Dalish are a historical enemy of the Chantry, and the cultural differences between herself and the Dalish Inquisitor may be too much for her to overcome. She'll be your friend, but she'll stop at that.
Do I think Cassandra will be race-gated in any way? No. But are these reasons that the devs could use to justify her being so? Absolutely. And they don't ave anything to do with race.
Personally, I think a character's religious stance will be more of a barrier than race or background. Given Cassandra's strong faith, I think that an Inquisitor who stands against the Chantry, or takes a severe Anti-Andrastian stance, will cause too much friction with Cassandra to bring on a romance. Does this mean you have to be Sebastian 2.0, or be a kowtowing, Pro-Circle, Pro-Templar mouthpiece? Hardly. But if you seek at every opprotunity to destabilize and dismantle the religion that Cassandra dedicated two decades of her life to, there's going to be issues.