Likewise with socialist/social democratic parties -- if they abandon all the tenets of socialism: worker control of capital, anti-capitalism, etc. but still keep the name... is it just that the content of the expression has changed? That seems a stretch.
However, I guess there's an argument to be made that "left wing" is so non-specific that it could do what you're saying. The phrase itself has its origins in the French Revolution with the Jacobins, etc. who were certainly not socialist. So I guess there's that.
But here's the thing. Many of the politicians called "left" in the United States don't even call themselves that. The right wing in the US calls almost everything "left wing". I stare in amazement at people who call Clinton or Biden "left wing"; they don't describe themselves that way, and actual socialists and left wingers don't support them (except grudgingly with their noises plugged when they have to vote).
But to the Tea Party and Trump types, they are "left wing." By which they just mean something pejorative
Contemporary Pope would probably be horrified if someone suggested to him to initiate a crusade against the unbelievers. The combination of Christianity and politics has shifted over time, there is much less hard force and much more sentimentality involved.
But that does not mean that Crusaders weren't true Christians while Francis I. is, or vice versa.
The traditional left is gone because its proponents died out, but before they died, they introduced the young wokesters into their parties. The shift from blue collar workers to academia took decades to complete and there is a clear continuity in the process. So I think the label still fits, only the relevant institutions changed their priorities.