I think the disconnect is less "some people think that the numbers on your character sheet affect what your character is like and some people don't", and more "some people believe that for some reason there's a HUGE gulf in competence between what an 8 represents and what a 10 represents, and some people recognize that +1 is not that big of a deal and roleplay accordingly."
If you roleplay your Int 8 cleric as being incomprehensibly stupid, you are actively roleplaying your int stat badly. That's because Int 8 does not cause you to be so dumb that you're totally helpless and feebleminded. It causes you to be imperceptibly less likely to succeed on an int check. If you play a game where int-based checks are actually an important part of the game in any way at all, it becomes immediately obvious that Int 8 is not incompetence. An Int 8 character will roll better than an Int 10 character almost half of the time, and the Int 10 character is supposed to be average. They'll even roll better than an Int 16 character on a pretty regular basis. If you're insisting that Int 8 means that you can barely string a sentence together and are just a total wreck at any and all intellectual tasks, you're going to create comedy moments pretty regularly as a result of the uselessly dumb guy doing better on intelligence tasks than people who are supposedly average or better.
Of course, this isn't an issue if you're playing a game where knowledge checks are never tested, and it's only a small issue if you're playing one where it rarely matters. In any game where knowledge is actually a relevant and important thing to have, though, you can't play an Int 8 character as being significantly below average in intelligence without regularly breaking the fiction, because they're not much less likely to roll high than a supposedly average character. Because -1 is basically imperceptible. To whatever extent there is a correct way to RP Int 8, it's to RP the character as being of average intelligence, because they basically are. (Most people who believe that 8 Int is Talks-Like-Cookie-Monster-Can't-Tie-Their-Shoes don't seem to think that 12 Int means that you're an incredibly gifted savant who wows everybody with their intellect, even though it's the exact same difference.)