What does "accidental" mean in the context Marx uses it in?

When Marx says accidental he is referring to the means in which a person acquires something without it exactly having been earned by that person. It is through fate or luck, though, that he or she received it. Marx uses this word a lot in context to what one generation inherited from the preceding one, more specifically the ideas and methodology of that generation which would ultimately lead to the separation of classes.

From reading the (very cryptic and repetitive) text, I would be inclined to believe that Karl mentions the inherited beliefs as accidental because we do not obtain these them of our own free will. It’s like they were just in the way, left by the previous generation, building up in mass and size with each passing generations, and we rammed into them. We shape our entire society upon these found beliefs, including and most importantly, the class distinction, which separates us all. This is what Marx really wants to bring our attention to. Because of the past shaping our present, because of years and years of “competition and struggle of individuals among themselves”, we have a separation of classes dividing and categorizing us all, between the higher and lower classes. It’s very possible that that accident might also refer to which class we were born into, whether into the bourgeoisie or into serfdom.

I think, in the end, that Marx is pretty much inviting us to transcend these “accidentally inherited” beliefs in favor of newer, more practical ones of our own choosing in order to avoid these kinds of segregations.