Okay these are my picks for the race gated Companions out of who has been announced and the few who haven't been announced
Cassandra- We really don't have a clue about her preferences since we its never been brought up, I agree with the people on her maybe wanting an heir to her name and really she doesn't come across to me as someone who would go for a Dwarf or a Qunari. Elves are tricky since they are seen as low class citizens So if I had to guess she could be race gated to just humans or humans and elves.
Cullen- I don't think Cullen would go for a Qunari at all and maybe not a dwarf either. So I could see him being gated off to dwarfs and Qunari. Or maybe just Qunari. Especially after what happened in Kirkwall since he was there during the Qunari attack and we all know Cullen doesn't forget things like that.
Varric- If Varric is a LI I could see him being gated to just dwarfs, he did say he wasn't attracted to humans and lets face it dwarfs are not very fond of elves and their frolicking. He also wouldn't be up to romancing a Qunari after what happened in Kirkwall.
Vivienne- Lets face it everyone thinks she is shallow, conceited and picky. She has a high ranking in the world and wants to go higher and I don't see her jumping in the bed with elves, dwarfs or qunari so I could see her only being interested in humans, or at the very most humans and elves.
Those are my picks.