You're overthinking it. Normalize simply means either to become normal (intransitive inchoative) or to make something normal (transitive causative). Whatever normal means in context (and there are a lot of possible contexts), the verb is simply a regular, transparent, combination of normal plus the inchoative/causative -ize.

@JohnLawler If that's the case, find me an instance of it being used in the new sense before 2000.

There isn't any "new sense". There's a new context where it's being used. Happens all the time.

The problem seems to be in the interpretation of "become normal" and "make normal" ; there are two: conform to an existing standard and adapt the standard so as to call normal according to the new standard what was previously abnormal. I believe that the definitions do not exclude the second possibility; so we are left with a term that is not quite specific. "Even "reduce to a norm or standard" could be interpreted along those two possibilities without stretching the words too much. "Return to normal" does not but it is just one part of the definition.

@LPH Would argue the same thing for radicalize: : to make radical especially in politics?

I’m voting to close this question because it's based on a misunderstanding of existing definitions, including meaning #2 in the MW definition cited in the question itself.

@ChappoHasn'tForgottenMonica Clearly not. It's specifically mentioned in a book on language evolution and an article at MW.com

@ChappoHasn'tForgottenMonica 2 : to make normal (as by a transformation of variables) This is referring to statistical normalization

Your question is based on a false premise as the so-called "new sense" you mention isn't new or even newer than the other sense but rather has always existed." Its Latin root from which its derived has both senses you mention, indicating it came into English with both senses, underpinned by its Romance language equivalents, like "normalizar" in Spanish and "normaliser" in French, have also always had both senses. I would suggest the false assumption that forms the basis of your question is the result of a phenomenon called recency illusion, a type of logical fallacy or cognitive bias.

@BenjaminHarman A team of specialists in the evolution of the English language seem to disagree.

I'm voting to close this question because it's based on an unfounded, false premise, specifically that the so-called "new sense" of "normalize is new, which it's not. The Latin root from which it was derived included and includes that definition. That definition likewise exists for cognates in other languages, like "normalizar" in Spanish and "normaliser" in French. Anglicized as "Normalize," it was imported with said definition, so the question is based on an unfounded premise that is false.

@BenjaminHarman It may surprise you to find that the Spanish "normalizar" does not carry the connotation of "to make something abnormal come to be considered normal." And neither does the French "normaliser"

That citation actually proves the opposite, that the so-called "new sense" isn't "new" but goes back at least to 1864. Meanwhile, the author of that 1996 citation fails to actually provide any citation from the actual OED but merely baselessly claims that the definition isn't there, much less provides a citation going back to 1864 OED, which is what would be required for that researcher to properly found that unfounded claim. I know it's false, though, as I have a 20-volume, unabridged OED on my bookshelf, published in 1989, Second Edition, that does provide that definition.

I didn't post the same comment twice. The first I posted to let you know about an issue with your question to give you an opportunity to redress it. The second I myself didn't post but was automatically posted by Stack Exchange when I voted to close the question 15 minutes later after you hadn't redressed the issue. When one votes to close a question, this cite requires an explanation, an explanation it then automatically posts in the form of a comment. Since my basis hadn't changed, the language in my vote to close is similar.

I did read that answer, and it supports what I said and the opposite of what your citation otherwise said-- that the OED does, in fact, provide the definition given and that, based on the citations it gives, the sense isn't "new," as you put it, meaning the answer you selected likewise informs you that premise of your question is false, albeit not in so many words. Just because you selected an answer in hopes of not having the question closed doesn't mean that it doesn't merit closing for it being loaded, i.e., based on an unfounded and false premise.

Why are people voting to close this? It's a very answerable thing. The OP doesn't know (and neither do most people).

Because it's based on an unfounded and false premise. It unfoundedly and falsely asserts that the given sense is "new" when it is not. Research is required to post questions. Research needn't uncover the answer, for if it did, there'd be no need for this website, but what it absolutely must include is foundation for any assertions made as part of the question's premise. This asker didn't do that, so the question includes a false premise, which, according to Stack Exchange, is grounds for closing it.

Meanwhile: "'Normalization' originally described a return to a state considered normal. Later, it was used to describe the act of making something variable conform to a standard. Recently, we've seen it used to describe a change in what's considered standard. In this new 'normalization', the standards change to make something considered an outlier 'normal'—not the other way around."

@Mitch Your question must be rhetorical, since two users have given explicit reasons for closing. Yes, it's answerable: "There's no 'new' sense."

By the way, there wouldn't be an issue if the question didn't employ "new," even emphasizing it with scare quotes, and had simply been, "When and where did this sense of normalize begin?" If the OP were to simply edit the question to remove the premise that the sense is "new," then the bases given for closing this question would dissolve away. That has been the point of all the comments, not to argue with the OP but to simply alert the OP to the false premise, one clearly based a recency illusion, a common cognitive bias, and edit the question accordingly so that it no longer includes it.

@BenjaminHarman "based on an unfounded and false premise." that's unkind and irrelevant reason to close. If the OP doesn't know then they are likely to make assumptions that are wrong. That's a very good time to answer and explain, when the OP doesn't know..

"Unkind"? It's not unkind. It's not attacking the OP. It's only indicating issues with the question that are noncompliant with EL&U's terms and conditions, issues to do with its premise. "Unfounded" is self-evident, it not being founded within the question or its explanation. "False" has been proven by multiple citations. There's nothing unkind about letting someone know the truth, that they've been wrong about something, not when it's constructive and required, which in this case it is as the question doesn't meet EL&U's requirements while left unaddressed and is thus subject to closure.

@Mitch No idea how to get through to these guys. They don't seem to understand that if they have the argument and evidence they should post an answer, and they don't seem to acknowledge that this very question has been tackled by Merriam-Webster in an online article and by experts in a book on language evolution. It's like screaming at a wall.

@BenjaminHarman Instead of reinforcing blind adherence to rules and button pushing, please readjust your threshold for closure because of someone asking a question that makes wrong assumptions. These are the kinds of questions that are interesting.