As others have said, it almost entirely depends on race.
Night elves, it would seem, are popularly depicted as being... flexible. This makes some logical sense, given that, even with a minimal non-druid male population, those on the Long Vigil probably got tired of parcheesi after a few hundred years. Blood elves might carry on this tradition, or they might not. Like several other races, there aren't many blood elves left, so some degree of encouragement is probably given to those relations that have the potential to bear children.
Draenei... well, popular opinion (meaning, if I see another pregnant #*@@!@# draenei death knight, I'm going to eat a goddamn baby) is that they're pretty open to things, but... they're arguably one of the most depopulated species on Azeroth. Heteronormativity is probably enforced purely to ensure survival.
Humans are The Mario of races, so it goes either way. Whatever you want, basically. Stormwind humans are probably pretty fine with it, Gilneans maybe not so much, given how tradition-bound and xenophobic they are. Other nations, I have no idea. Lordaeron's shtick was religion, but we have no idea what the Holy Light's stance is on homosexuality - given how progressive it is when not being worshipped by Scarlets, I'd say it doesn't have one.
Gnomes, I'd say they simply wouldn't care. There's the argument of their depopulation, but they apparently breed like rabbits. They don't really have hard-set traditions, and it's frankly hard to imagine gnomes being intolerant of anything other than maybe leper gnomes.
Dwarves... hm. Frankly, there's nothing to go on here. My instinct would be to say they might frown on it, since dwarves (in other settings, and possibly Azeroth) often are described as not reproducing very often, meaning that using the few occasions you can to do so is probably pretty important for the survival of the species.
If you're noticing a recurring pattern, good. Races that have population or reproductive issues are more likely to be less welcoming of homosexuality, because making sure there -is- a large next generation is very important.
Forsaken don't get nasty. End of story. They lack every single biological function that would be required. This probably kills most of their sexual and romantic drives, though see humans.
Orcs, eh. I could see it, I guess. They're not in danger of depopulation, certainly, and there's nothing about their culture that would really suppress it. A throwaway quest from pre-Shattering barrens implies that the Horde was fairly sexist before Thrall came along, though, so it may hold similar attitudes about homosexuality.
Trolls... probably. Like gnomes, they're implied to breed like rabbits, and it sort of fits with their unrestrictive culture, I guess. There's not much Darkspear troll culture to go off of, though, so... it's unclear. On the other hand, they're a tribal society with massive population issues (the smallest population of any playable race). It could go either way.
Tauren; very unclear. Their romantic traditions are almost never mentioned, though some of Cairne's comments in the Shattering imply that it's considered normal for young tauren to be interested in the opposite sex. Other than the Grimtotem, they're pretty accepting of new traditions (Sunwalkers, Cenarian druidism), so... maybe.
Goblins. I'm not even going to go there. Quote: they're totally into that.
Night elves, it would seem, are popularly depicted as being... flexible. This makes some logical sense, given that, even with a minimal non-druid male population, those on the Long Vigil probably got tired of parcheesi after a few hundred years. Blood elves might carry on this tradition, or they might not. Like several other races, there aren't many blood elves left, so some degree of encouragement is probably given to those relations that have the potential to bear children.
Draenei... well, popular opinion (meaning, if I see another pregnant #*@@!@# draenei death knight, I'm going to eat a goddamn baby) is that they're pretty open to things, but... they're arguably one of the most depopulated species on Azeroth. Heteronormativity is probably enforced purely to ensure survival.
Humans are The Mario of races, so it goes either way. Whatever you want, basically. Stormwind humans are probably pretty fine with it, Gilneans maybe not so much, given how tradition-bound and xenophobic they are. Other nations, I have no idea. Lordaeron's shtick was religion, but we have no idea what the Holy Light's stance is on homosexuality - given how progressive it is when not being worshipped by Scarlets, I'd say it doesn't have one.
Gnomes, I'd say they simply wouldn't care. There's the argument of their depopulation, but they apparently breed like rabbits. They don't really have hard-set traditions, and it's frankly hard to imagine gnomes being intolerant of anything other than maybe leper gnomes.
Dwarves... hm. Frankly, there's nothing to go on here. My instinct would be to say they might frown on it, since dwarves (in other settings, and possibly Azeroth) often are described as not reproducing very often, meaning that using the few occasions you can to do so is probably pretty important for the survival of the species.
If you're noticing a recurring pattern, good. Races that have population or reproductive issues are more likely to be less welcoming of homosexuality, because making sure there -is- a large next generation is very important.
Forsaken don't get nasty. End of story. They lack every single biological function that would be required. This probably kills most of their sexual and romantic drives, though see humans.
Orcs, eh. I could see it, I guess. They're not in danger of depopulation, certainly, and there's nothing about their culture that would really suppress it. A throwaway quest from pre-Shattering barrens implies that the Horde was fairly sexist before Thrall came along, though, so it may hold similar attitudes about homosexuality.
Trolls... probably. Like gnomes, they're implied to breed like rabbits, and it sort of fits with their unrestrictive culture, I guess. There's not much Darkspear troll culture to go off of, though, so... it's unclear. On the other hand, they're a tribal society with massive population issues (the smallest population of any playable race). It could go either way.
Tauren; very unclear. Their romantic traditions are almost never mentioned, though some of Cairne's comments in the Shattering imply that it's considered normal for young tauren to be interested in the opposite sex. Other than the Grimtotem, they're pretty accepting of new traditions (Sunwalkers, Cenarian druidism), so... maybe.
Goblins. I'm not even going to go there. Quote: they're totally into that.