Two things can be true at the same time. Was it "culture" that they were trying to destroy or restrictive ways of doing things, that could be better attributed to "customs" and "habits". "Culture" was the word that it was translated to in the West, but custom and habits is a better description. Remember the "4 Olds ( 四旧)"?
And yes, they really did try to erase examples of the past. Maybe not Mao himself, but the Red Guards did. Right across the street from Beilin is Wolong Temple (founded around 200AD). The Red Guards ransacked the temple and forced all the monks there to kill themselves.
And no, this was not like the past. Do you remember who and how the Red Guards and their extremism were finally stopped?