[Dr. Franklin]

No, her use is correct. In this sentence, “they” represents the voters and “their” replaces “his or her” own grievances.

No, she misspoke. What she intended to say was:
They want that person [Trump] to talk about the people’s grievances and not their his own.

[EEGator]

You’re vindicated.

[the OlLine Rebel]

That is common ignorant, lazy abuse of the language. Not wokeness. Everyone does that bad usage. All my life it’s been typical.

[TheWriterTX]

If we look at the larger context, she was referencing candidates (plural) in general and not Trump in particular. Because the noun was neither identified as a man or woman, she used the correct pronoun.

I understand your concern and I presume that you can find verbal hiccups irritating. Phrases such as would of, could of, should of, ain’t, kinda like, and people that put themselves first (me and my friend, I and my mom) all grate on my nerves.