It’s actually more common than you’d think for HC stories to just… let you not be romantic. Like, I can name four off the top of my head where I got away with not really doing anything romantic with anybody.
In Never Date Werewolves, you can choose to play your character as a single mom with six kids, a job, and no time or interest to even think about dating. It turns from a romance game into a slice of life dramedy about single motherhood! (In a world where werewolves exist, but still.)
In the pirate game whose name I’m blanking on, you frequently get hit with situations where you see couples being cute with each other, or the game throws questions about your take on romance at you, and there’s always at least one answer that’s essentially, “man, who cares? I could be doing pirate stuff right now.” I don’t know if you can actually dodge the romances, since my character picked a fight with Caleb in chapter ten and got Mike Tyson’s Punched Out for the SNES, and starting the whole story over from chapter one didn’t sound very appealing to me.
In Belle-De-Nuit, I may have been too focused on channeling my inner Puss In Boots, but I can’t recall where any of the romance triggers were. I did, however, spot all the points where I could engage in an honorable duel, and jumped on them, because I am a closeted musketeer.
In If It Please The Court, you can pretty neatly dodge romance stuff in favor of purely focusing on the spy games and political intrigue. Of course, my character wound up fleeing to Poland because she turned traitor to the French crown, but I mean hey, shit happens, right?
Those are the four I’ve played that I know do that. Haven’t really touched any of the others, so can’t confirm or deny on their count.