vaiselle is actually inhereting its gender in an unrelated manner.

It comes from Latin vāscellum which is a Neuter noun.

But the specific form that gave rise to vaiselle was the collective plural of that noun vāscella. source

And it’s a common pattern that in vulgar latin, (what gave rise to french), collective plural nouns were interpreted as feminine. I think this is a general tendency and unrelated to the noun’s meaning. The reason often given is that neuter plural endings and feminine singular endings were the same in Latin.

BTW; this is also the latin root of the english word vessel.

(PS: I agree with you that gender in language is problematic and I prefer non gendered as well).

Vaisselle is feminine, but lave-vaisselle is masculine.

Une lave-vaisselle totally does not work.