I guess my problem with saying that it's a fallacy to claim that RP and charop are never incompatible is that that implies that one's criteria for the two are absolutely inviolable--that we can in fact treat them like utterly rigorous, hard-edged "sets." This seems...rather un-like how I do my own attempts at them, and I expect that at least some others are the same. (It's tempting to argue that many or most are, but that could just be projection.)
That is: How can you be sure that, when a conflict is discovered, people absolutely *can't* relax one or both requirements such that the "rigorous set" analogy fails? If you can't be sure of that, then it seems like it's a fallacy to say "RP and charop are never incompatible" if, and only if, you add to it "and your priorities are not flexible."
Sometimes, I'll make a compromise that sacrifices some small amount of roleplay, if the charop benefit is substantial and meaningful. For instance, I generally like to spread my stats around more, rather than hyperfocusing on one or two of them. But let's say we have a hypothetical game where HP are an incredibly precious resource--difficult to acquire, difficult to restore, easy to lose--and I have a choice between a boon that would double my HP, or one that would teach me a new unusual (e.g. not typically seen in the campaign) language and provide an extra academic skill (e.g. Nature, Arcana, History, etc.) The HP is clearly the more powerful of the two choices, but the amount of long-run roleplay that can be had from the latter is relatively minimal. The HP will also give me a substantially greater assurance that I will survive to roleplay more with the character I already have. Since it's difficult for me to rapidly switch gears between characters (I find PC death, my own or others', rather demoralizing), the former choice seems like a substantially better choice--without much of a roleplay sacrifice.
On the flipside, as stated above, I really prefer my stats to be spread around--and while I love playing Paladins, I hate the idea of playing a "Paladunce." So I generally avoid dumping Int if at all possible--and, given the Paladin's stat requirements, that usually means scavenging from Dexterity instead. That's a clear charop sacrifice--every guide I've ever read, ever, puts a premium on Initiative, putting it only just behind "do you successfully hurt things" stats. But I'm okay with that sacrifice. If anything, it fits the character--someone who is very deliberative, who thinks before acting.
More or less, I'm getting the idea that people are viewing Charop and Roleplay as though they were like "virutes" in ethics--and then arguing that you obviously have to value one categorically over the other, and thus cannot say that both are equally (part of) "the good." I reject both of those lines of thought: the two are not totally incommensurable, and I don't believe it's true that at least one of them has to be rigid and inflexible. Both can--and should!--bend, adapt, and reconsider, at least *some* of the time...especially when the two appear to be at odds.