I'm really doubting the race-restrictions would be story-based. I mean, I'm sure they'll work them in, but I'm gonna guess the reason they might exist at all is the technical one.
Not wanting to animate 8 cutscenes for 6 or more character models is completely fair in my book. So long as the restrictions make sense (the aforementioned Iron Bull restrictions, for example) and everyone still gets a decent amount of options (ie Dwarves and Qunari aren't screwed over) I'm cool with it.
Yeah, I'd guess technical reasons trump story reasons, but story reasons would be aces.
The rest is ALL hypothetical-
Varric wasn't gonna get with Hawke. Lets assume that was because Hawke was human.
Qunari after DA2? No way.
That leaves elves and dwarves, and I think you can take off dwarves if you just say that Varric is attracted to his own race.
FemDwarves rejoice, the chest hair is all yours.