Which of those are inheritable?
I don't know about the bee or mushrooms, but basically everything but the slimes and possession. The kids will be a "half-beast" with traits of the beast that got the parent pregnant. I think if both parents are the same race it just makes the classification a full beast-man. But visually the same, I.e. bunny traits if the mother was impregnated as a bunny-girl. The harder ones to get would be the bunny, cat, and dog traits since there isn't a potion or enemy for them yet so someone has to be corrupted.
Possession is kinda weird since it's a ghost that takes over a party member for a few turns with a strength of 1-3. 1 being slight physical alteration depending on the color of the enemy name (blue more masculine, pink more feminine) and 3 being a total sex conversion. But I haven't had any female party members be impregnated so not sure if that causes any trait passage. Pink doesn't come with a womb, so they can't get pregnant by default. I kinda feel like the changes should last after the possession ends, but I also can see why that isn't a thing.