I had written a response to the post above this but I hit the wrong reply button and lost it. Which is frustrating, and this will be brief.
First of all, genetics is simply the biochemical mechanism of heredity. You can't have heredity without genetics, and genetics causes heredity. They are, in effect, the same thing. Any argument to the contrary is simply arguing semantics, and as someone who has studied a fair bit of biology and genetics, I'm just not interested in arguing over niggling semantic disagreements.
Two, Mendel's work was vital. Yes it was lost and then rediscovered, but it wasn't rediscovered -after- genetics had been explored; his experiments were the key piece that set off a revolutionary way of thinking about heredity as a function of genotype versus phenotype, and if you don't think that's foundational in modern genetics, then you don't know anything about genetics at all. Suffice to say, the biology faculty at my university disagrees with your notion that Mendel's work was useless.
I brought up Mendel to draw the very obvious link between heredity and genetics. He was, after all, that took the concept of heredity, which is a concept that has existed in documentation for close to two thousand years, and set off the scientific study of heredity; ie, genetics. I thought this was clear.
Finally, it doesn't really matter, y'know, to me whether the people of the middle ages had some basic understanding of heredity, or whether they thought that people were liable to give birth to baby pigs. It really has no bearing on whether or not I think that a genetic component to attributes has a place in the game. I would like the game's engine to be as historical precise as possible. If the players want to manipulate it that is their choice. If they choose not to, that is also their choice.