Yes, and Brouwer lost that fight. Classical logic is an implicit assumption for professional mathematicians. LEM is simply taught as the truth in university courses. My SO who is a math phd student hadn't even heard of intuitionistic logic before.
If you want working mathematicians to use theorem provers, they need LEM. But this isn't actually all that much of an issue, since you can just introduce LEM as an axiom. It breaks computationality, but it's not like proof assistants using classical logic would have this either.
So is[0] the notion that quantum systems magically undergo non-local, non-linear, non-unitary, CPT-violating, Liouville's-Theorem-violating, non-deterministic evolutions whenever a macroscopic system that happens to implement a sapient intellegence looks at something[1]. So that's not a very good yardstick for "this is not obviously false".
0: sample size of one univerity (circa 2010) for "simply taught as the truth", but I think it's recent enough and widespread enough to make a good example. See [2] if you want to investigate further.
1: aka the collapse postulate or Copenhagen interpretation
2: https://en.wikipedia.org/wiki/Copenhagen_interpretation#Acce...