You are right. They are as close to being liberal as we are
to being ultra right wingers.
And even beyond the fact of it being a lie, which is bad enough, we are giving them political power by allowing them to frame the debate in advance, by letting them get away with this disingenuous redefinition of words. It seemed a small thing in the past, unworthy of notice, time, or correction, something to just brush aside in order to get to the meat of the matter, but now allowing them to define words to suit them is coming back to bite us in the azz.
Not to mention the way we always wind up dancing to their tune because they keep moving the goalposts as a distraction from the issues. Just look at the absurdity of the way we went from “colored people”, through various other terms, only to arrive at “people of color”. While we were busy acceding to each new term, playing defense, we were losing control of the right to mean exactly what we say, instead of having the left define our words for us.