A hypothetical question: In a fantasy world that’s kind of based on medieval Europe, but in which the genders are considered completely equal (with all the rights and duties that come with that). If a minor noblewoman were to marry a rich merchant or craftsman in this universe, would their children be considered nobles as well, or would they be commoners?

Hmmm…

I mean, a medieval Europe where the genders are completely equal would be so radically different that I don’t know whether it would be recognizable as medieval Europe (in which case, why not have a fantasy world that’s its own thing?), especially given the strong ties between patriarchal conceptions of the family and inheritance of land and military/political power by blood descent.  

But to answer your question, I could see arguments for either case. In a truly gender egalitarian medieval world, there would probably be less emphasis on status flowing from the father, so the argument would be that the child of a noblewoman is a noble because their maternal parentage isn’t (usually) open to question. On the other hand, if noblewomen’s rights (especially inheritance) were equal to men, I would imagine there would be a cultural fear of noblewomen getting snapped up by ambitious social climbers, so elites might establish a custom that children would be born common as a disincentive.