Yup... it's weird. I have 'SuperSims' that I mentioned before with all of the previous 'occult' possible born-with traits and they also had the alien handshake (details on that in my previous comment). So... it must have to to do with an active occult, and that the alien trait must always be active. However, I can have the sim actively any other occult while having the alien handshake trait. This fairy trait is the exception. So I went back through the 'SuperSim' 'breeding' process, but this time all I left out was the alien ancestor (many generations back) so the infant does not have the alien handshake when she gets to teen or older. So, she has the 'born with' traits of Sulani Mana, Ancient Bloodline, Greater Wolf Blood, Father Winter's Baby, & was Conceived in the Lighthouse. I tested her by aging her up and she is able to plant the fairy seed, be a fairy, and even have an offspring with the High Fae Lineage trait if the father is a fairy. However, if she has this baby with a fairy father the baby only inherits Sulani Mana,& Strong Bloodline from mom.
https://www.ea.com/games/the-sims/the-sims-4/pc/gallery/25B4F64A98454AEFB055979F6A914350