It seems to be a show-only thing. After all, there have been a number of very prominent LGBT figures in the history of Westeros – Laenor Velaryon, Prince Daeron, Daemon II, etc. – and you’d think that if it was as significant a sin as it is on the show, it would have come up when these figures were potential candidates for the Iron Throne.
However, there doesn’t seem to be widespread social acceptance either, given that (for example) the majority of the LGBT characters we encounter get married to people not of their sexual orientation, although this seems as much (if not more) about pulling their weight in their family by producing heirs and making dynastic alliances as it does about remaining closeted.
Indeed, if we can take Cersei’s ruminations about Renly as any metric, rather than seeing sexuality as something set in stone, it seems to be described as a general preference but not an exclusive one: “a man may prefer the taste of hippocras, yet if you set a tankard of ale before him, he will quaff it quick enough.”
Do we have any idea how this plays out among the smallfolk? All of the examples of gay westerosi that I can think of are highborn, which might give them the freedom to be a little more open about it, especially since dynastic marriages and children are expected regardless of your romantic preferences.
Satin, for instance (who may not, of course, be gay) gets disrespected a fair amount at the Wall. It certainly seem possible that the social stigma around homosexuality is a much bigger deal without the privilege of social class. Moreover, it seems as though The Faith of The Seven, with its well defined gender roles, is a lot more militant among the lower classes of Westeros, which could add to the social stigma of LGBT Westerosi smallfolk.
Speaking of which, lesbians seem a lot thinner on the ground in Westeros than gay men. presumably this indicates some additional social stigma? I’d suggest that it’s similar to the class issue, another kind of privilege that men have that is denied to women.
Gay smallfolk…hmmm. Well, I think Varys and Illyrio were ex-lovers, but neither of them are Westerosi. In terms of smallfolk attitudes, no one at the Wall seems to bat an eye at Alf of Runnymudd and Garth, altho some are disrespectful of Satin. This might be a hypocrisy angle common to many societies – that the older, presumed top, partner is acceptably manly, whereas the younger, presumed bottom, partner is seen as having taken on the feminine role and is scorned not so much for having sex with men but being too femme. (See George Chauncey’s Gay New York for how this viewpoint continued through the early 20th century)
As for lesbianism, I think this is a weird offshoot of patriarchy, namely that women’s sexual desire isn’t deemed as something important (as long as it’s not screwing with male line of descent). Hence the Bible doesn’t mention female-female sex while it does discuss male-male sex, hence Japanese texts from the Medieval period through to the 18th century having a well-worked out typology for male sexuality while largely ignoring female sexuality outside of the male context.
So to go back to Westeros, no one blinks an eye at the idea that highborn women might have their handmaidens sleeping in the same bed (whereas they’d freak out at the idea of an unmarried highborn women sleeping in the same bed as a man), and neither Cersei nor Dany seem to have any conception of any taboo existing when they have sex with women. And if we take Lady Sabitha Frey nee Vypren, the fact that she was “fond of…kissing women” seems to have been treated as a kind of outgrowth of her performing other aspects of masculinity like wearing armor, riding horses, and fighting in battle.