What "new policies"? You have yet to identify an actual company/university policy that you or her or her husband finds questionable. Earlier you said that she was one of your employees, and now you say that she was frustrated with "new company policies," so it would stand to reason if you are her manager that you would know what policies she might be talking about. And obviously it seems like you have concerns about these mysterious policies too.
Let's make it easier: if you can't identify your own company policy that is causing so much consternation, then let's identify any policy that any reputable company, corporation, or university has (public universities typically post all of their policies online), that you feel is representative of cancel culture or is too woke. Then we can discuss what is unreasonable about these policies and how they can be changed. Is that fair?
Language evolves, and sometimes it evolves rather quickly. Let's use psychiatric and disability language for example. Back in the day, doctors and psychologists used words like "idiot" and "imbecile" as actual medical terms. I think these words were even used in early versions of the DSM Manual (I may be wrong, feel free to correct me). Later, these words became commonly used as pejorative insults, so the language changed. For many years, the R-word was used instead. It became used in a derogatory way as well. So language evolved again, and we don't use the R-word anymore (unless you are intentionally being an a$$hole).
Now think about the word "queer." That word has been used as a derogatory term for a hell of a long time, but has largely been reclaimed by the LGBTQ+ community (that's what the Q stands for) as an acceptable term, but the context regarding how the word is used still matters. Not everyone in the LGBTQ+ community likes that word, and it can still be triggering to some. And it can still be used inappropriately.
With pronouns, the vernacular has changed really quickly, and it is hard to keep up. So when you mention "Pronouns or phrases they used for decades," let's talk about "they" as an example. You and I likely grew up using "they" as nothing more than a plural pronoun and not as someone's personal identity. It still feels weird to use "they" as a singular pronoun instead of "he or she." It doesn't sound like the proper English that we learned. But times have changed. Is there a reason to stubbornly dig your heels in and refuse to use "they" if that is what someone prefers? What harm does it do to you to learn to use a word a little bit differently? What harm does it do to the older man in your example to refer to professional women as "women" instead of "girls?" It does no harm at all to make that change, but using respectful language or using someone's preferred name or pronouns can show that you are making an effort at respecting them.
Let's think critically about this a little bit further. In the business world, a "reprimand" is typically a disciplinary action, right? Does a union boss have the authority to discipline? Isn't the job of a union leader to look out for the fairness and just treatment of their fellow union members? Further, can you think of any real policy that would lead to someone being disciplined for mistakenly calling someone "girls"? Is it more likely that this was an educational conversation with the older gentleman? Now, if you said something that unintentionally offended someone else, wouldn't you want to know about it?
What happens when that same older man makes a mistake in any other aspect of his job? Does he learn and improve, or does he just stop doing his job? Look, when we make mistakes (and we all make mistakes), we need to acknowledge the mistake, suck it up, and do better next time. That's not too much to ask.
Again, let's think critically about this situation. There is a huge difference between a reprimand, and "huge trouble," versus a conversation with the Dean or more training. Hell, we all need more training, that is not a bad thing. And a conversation with the Dean is not a disciplinary action. Call it conjecture or call it critical thinking, but what do you think actually happened in this situation? Think about what is reasonable. Is this really what "cancel culture" is?