> And yet, we as a civilization can still benefit from "math proofs" in spite of the fact that there are some philosophical differences on what "proof" is.

Not really. You don't generally benefit from proofs being correct. You benefit from something you think is correct works well for your purposes, and it usually isn't proof itself, but some result derived from it. It's actually considered even paradoxical, that our math "works so well" despite of very foundations of it being proved "not working". It's like… well, I cannot remember good enough example right away, but consider different folk beliefs: many of them are actually pretty good advices, but not because there are some true reasoning behind them, but simply because they advice to do something in some situation that occurs to be helpful in case of phenomenon which in real life often occurs along with described situation. So some enlightened gentleman who is against silly superstitions and can show that "proof is incorrect" only suffers from that, because despite "proof being incorrect" the adviced behavior is still the safest one.

And by the way I don't only mean "philosophical problems" like ones we've got after Goëdel. I remember being told when I was a kid that mathematics are very old science, that it was used and developed by ancient persians, egyptians, etc. And, well, it was. So years later I was really, really astonished to learn how frivolous to say at least that "mathematics" was. Many things that we know as theorems today weren't actually theorems back then (which isn't surprising by itself, because the mathematical notation itself is very late invention, but I expected the essence of it to be the same), but more like beliefs or pretty redundant technical recipes on how to make this or that thing done. Even one comparatively late and "truly mathematical" text — Euclid's "Elements", that is, — isn't without faults. Many of his proofs weren't proofs by any today's standards, or even by standards of 100 years ago. Many of his very basic statements were dismissed later as being redundant or incorrect or simply pointless in the sense that "they mean nothing" in the context of maths. Still, as you know that work of his was quite helpful for later generations.

> Those are 2 very different sentences and I did not write what you think I wrote.

Actually not, I didn't think what you think I did think you wrote. I understood you correctly. I said that ["best practices" are not disqualified because of disagreements] isn't the most correct thing to say, because if there is disagreement between adepts of "best practice A" and contradictory "best practice B" it's very much possible — even likely — that "best practice A" could and should be disqualified in favor of "best practice B", because the second one is objectively more beneficial (and then it would be "disqualified because of disagreements" indeed). Yet because world isn't black and white "best practice A" could also be working, so if you stick with A it could be better than nothing at all.