Don't bother mate. Even if you corner them on something, they absolutely will not budge.

I like many others brought up calculators and how common basic calculators only evaluate from left to right. They contend that this is not true and that calculators have always been able to obey order of operations. I even linked the manuals of two different calculators which both had this operation.

He asserted (without evidence) that the first does not operate in this way (even though the manual says that you must re-order some expressions so that bracketed sub-expressions come first). He then characterised the second as a "chain calculator" for "niche purposes". So he admits it works left-to-right, but still will not admit that he was wrong about his claim.

This calculator thing is not central to the discussion on order of operations, but it goes to show: you will not convince him of anything no matter what the evidence is.

By the way, after reading a few of his comments, I believe I can summarise his whackadoodle understanding if you want to continue tilting at windmills: he fundamentally cannot separate mathematics from the notation. Thus he distinguishes many things which are the same but which are written differently.

• He calls a×b multiplication and ab a product. These are, of course, the exact same thing. Within a mathematical expression, the implicit multiplication in ab can, by some conventions, have a higher precedence than does the explicit multiplication in a×b, and he has taken that to mean that they are fundamentally different.
• He thinks that a(b+c)=ab+bc is something to do with notation, not a fundamental relationship between multiplication and addition. (This is not a difference for him though). This he calls the "distributive law" which he distinguishes from the "distributive property" (I will say that no author would distinguish those two terms, because they're just too easily confused. And many authors explicitly say that one is also known as the other). He says that a×(b+c) = ab + bc is an instance of the "distributive property".

A “teacher” who doesn’t know that all lessons are simplifications that get corrected at a higher level,

As opposed to a Maths teacher who knows there are no corrections made at a higher level. Go ahead and look for a Maths textbook which includes one of these mysterious "corrections" that you refer to - I'll wait 😂

refers to children’s textbook as an infallible source of college level information

A high school Maths textbook most certainly is an infallible source of "college level" information, given it contains the exact same rules 😂

A “teacher” incapable of differentiating between rules of a convention and the laws of mathematics

Well, that's you! 😂 The one who quoted Wikipedia and not a Maths textbook 😂

A “teacher” incapable of looking up information on notations of their own specialization

You again 😂 Wikipedia isn't a Maths textbook