Grimdark - it varies hugely by campaign, but I generally can't maintain the level of seriousness necessary for GRRM Grimdark - my default tone tends to levity even when horrible things are happening, as in Fritz Leiber's Swords saga.
Also while Martin is great at depicting realistic consequences for stupid behaviour, I don't generally have my good-guy NPCs behave as stupidly as he does. In particular, even Lawful noble houses have had a lot of experience at not dying, and a lot of selective pressure for not dying, too. So the kind of level of grotesque incompetence displayed by the Starks in the TV show would be vanishingly rare IMCs. I tend to have the Lawful Good guys be just as capable as the Littlefingers & Lannisters - they may not engage in the same kind of behaviours, but they are aware that other people may do so and can thus usually take account of it as a possibility in their own plans.
Sex - a few of my campaigns have about as much sex as the HBO show, most have much less. Usually the sword & sorcery type campaigns have relatively more sex (and certainly more nudity), but my Forgotten Realms game has some sex, in a nod to Ed Greenwood.
Romance is fairly frequent in most of my campaigns. I tend to avoid 'doomed romance' tropes, I definitely avoid the 'girlfriend in the fridge' trope of killing a romantic interest NPC to motivate the PC. That sort of thing is best left to a PC's backstory.
Rape - in my more adult games NPC characters may be implied or (rarely) stated to have been raped. I've never depicted forcible rape 'on screen' in any D&D campaign, which is pretty much the same as the HBO show. I have a hard 'no raping the PCs' (male or female) rule. I will look for ways to make this plausible in-universe. If a player were to insist on putting their PC into a situation where this was a likely outcome I would work with the player out of game to discuss what they wanted and what should happen - basically unless the player has consented, the PC cannot be raped. In lighter-themed settings NPC antagonists generally either have a code against rape (eg chivalry, for human types) or no interest in it (eg for non-humans).
Food -I try to describe the food & drink to help get a feel for the setting, especially if it's significant - eg in one campaign nobles compete to lay on feasts for guests as a sign of prestige.
Gore - generally the swords & sorcery campaigns have more gore, the Palaces & Princesses campaigns don't have viscerally described gore. My described gore levels may be similar to the HBO show in the most adult-oriented games, but usually less.
Sexism - gender role differentiation IMCs tends to be less than IRL, but I don't make a Paizo-style fetish of avoiding it. If there are female players I try to keep an ear out for what they want - eg it's very common for players to want an 'overcoming entrenched gender norms' theme for their PCs, usually in the lighter more Palaces & Princesses themed games like my current Karameikos game. If players don't want their PC to face any gender-based obstacle I'll work with that, too. I'm generally more considerate of the feelings of female players here because they tend to bring in more baggage from real life, and for D&D I think players should be able to play a PC of their own sex if they want without being disadvantaged thereby.
Homosexuality - I tend not to use historical medieval attitudes to male homosexuality (and there's no ancient Greek style pederasty - not a trope in GRRM either afaik). My default setting is something like Western Europe ca 1995, or the very early Paizo stuff - no 'gay marriage', but no persecution either. There's a male homosexual NPC couple in my Loudwater Forgotten Realms game, who 'came out' at Lady Moonfire's summer ball, at the same time Lady Moonfire 'came out' by being escorted by her Tiefling girlfriend Tawny Kytra.
In my Karameikos game my son Bill (age 7 3/4) playing his Baron William PC was annoyed that the Baron's daughter Hope, instead of submitting to the usual arranged dynastic marriage, was smitten with the roguish Elf Sea Captain Anastasia and threatening to sail off with her. At one point he threatened to 'ban being gay' in his Barony - which I think would have gone down badly with some of the other (adult) players! - but he was talked out of it, in-game by the Baron's wife. Instead he bribed Anastasia with his Medallion of ESP to go take a hike. Some 'mature themes' but the overall tone was much lighter than GRRM.