They really aren't. The only time they typically are is (VERY rarely) when high Cunning gives the PC a snarkier response or a witty one-liner. There aren't Persuade checks or things like that much if at all.
I only mean small dialogue variations, nothing major, but I do find it a tad annoying since I like customizing my characters roleplay, so dialogue variations that show your PC being strong for say, an amazonian character not being available if you are a charmer or mage since you can't level that attribute up at all. I'm just nitpicking, it's not a huge deal per say.
I can't speak for the whole game, but starting out there was breaking open the cage/pickpocketing/lockpicking in dog days, agility running with the woman in the track field which you get locked out of with pregnancy, and looking at the wiki a fair few scenes are described as requiring a certain amount of stats to accomplish like a rockslide, quests like Into the Closet/Shades of the Past which use the various stats for different outcomes, or bridal carrying an npc.
Plus it seems like backgrounds provide unique flavour text as well, although ones like scholar seem to get a lot more than the others, whilst some get none.
I completely understand that for most of these there are alternate options and you always have one or more that work (although it is probably awkward for a Meadow esque character if you play a Thief or Charmer), I don't consider this a huge deal, but it would be nice if roleplay dialogue wasn't directly tied to combat stats.