No it wasn't (and no it isn't), it's aimed at abolishing the class structure.
>There are people who don't like the current structure and aim to replace it. How is this a conspiracy?
GP is referring to "cultural Marxism" being a conspiracy, and it is, not that Communists want to replace the class structure. The "cultural Marxism" conspiracy theory posits that there is a group of people who want to destroy Western society. This is false. It relies on the idea that at some point Marxists changed to thinking in terms of gender or race rather than class - this is also false and lacking in evidence as GP also noted. The Wikipedia section really is a good overview of it.