Marxism simply suggests that socialism is the inevitable follow-up to capitalism. It is not about individual rights but rather the right of what is best for all. The needs of the many outweigh the needs of the few, or the one - schtick.
Right now, many liberals are advocating equal rights through what they call "marxism" when they're actually diametrically opposed when it comes to individual rights verses societal rights. Societal rights would actually fall under a kind of theocratic or set of moral standards. Either through religious dogma, or it can be subplanted by populist idealism. What we're seeing now between the two extremes of the parties is populist idealism of social justice being countered with another kind of populist idealism... anti-social justice, moral justice, or simply national-socialist (with the socialist part being VERY quiet on the right).
The right are socialists as well, they just are more Stalin than Lenin in their socialism. Lenin advocated for the sepeartion of church and state; while Stalin sought to control the nation through religion; denouncing and destroying all religious opposition and demonaninations and then later reviving the Russian Orthodox Church. True, the right are not shooting hundreds of millions of catholics or jews; but they don't need to if the state conceeds their power in the name of religious freedoms.
It is very telling that conservatives view equal rights or even the rights of minority groups as being granted more rights; rather than the same rights. Because this is them projecting exactly what religious freedoms mean to them. More rights to the majority, less for the minority.
Yet, that is precisely what the left ARE NOT advocating for. Nor even what is best for all. They believe individial freedom is best and that there should be little to no intereference from the state. There are inconsistences, of course. Their position of free speech, I think, is ultimately self-defeating. However, the accusations levied from the right that the state is controlling misinformation and hate speech through media is exagerated. Media is controlling speech, don't get me wrong, but this is not through state control but rather... again... populist idealism.