I'd think among the City-States it wouldn't be all that uncommon that such romances would be attempted. However, attempts don't mean successes and I'd wager it'd be more common among adventurers than anyone else.
The two races I could see have a problem in general with interracial relationships are Elezen and Miqo'te. Funnily enough, they're the two races who's two "clans" had direct opposition in their history (WW/DW feud over the pact with the Elementals, Keeper/Seeker thing that might have happened but I don't know Miqo history).
And even then, you have societal norms to consider as well - I'd say there's more of a chance between an Ishgardian Elezen and Hyur to shack up together (all vs. the dragons) than the same combination in, say, Gridania.
Lalas would likely be the race that have the least problems.
The two races I could see have a problem in general with interracial relationships are Elezen and Miqo'te. Funnily enough, they're the two races who's two "clans" had direct opposition in their history (WW/DW feud over the pact with the Elementals, Keeper/Seeker thing that might have happened but I don't know Miqo history).
And even then, you have societal norms to consider as well - I'd say there's more of a chance between an Ishgardian Elezen and Hyur to shack up together (all vs. the dragons) than the same combination in, say, Gridania.
Lalas would likely be the race that have the least problems.