I sometimes peek my head into chud communities and they actually do this too, sometimes with weird funny parallels to what we get. It's why the term RINO exist. They will frequently accuse conservative figures of secretly being too liberal or too socialist. It was actually frequently mentioned by some who were critical of Trump before he got elected, he was called a New York liberal, etc. Chuds also absolutely accuse liberals of lying and actually being Marxists (don't laugh!)
Libertarians do this too, frequently accusing their own of being statists or socialists for the smallest violation of ideological purity.
Liberals and conservatives have to accuse us of lying about what we want because we often have political demands that align with theirs, especially if they're working class, and that causes cognitive dissonance. So the only mental strategy they have is to accuse us of trickery. They'll make childish analogies like saying socialists want everyone to have a pony, or they'll say our demands are so extreme there must an equal price to pay. As in, for every gain in rights for the working and poor, there must be an equal loss in rights.