It is however so strongly inadvised (and bear in mind counselling prior to undertaking sperm or egg donation) - the chances of it actually happening are minimal.
If people are genuinely concerned about probable incest, please don't start with donor conceived children. That isn't where incest lies. Incest - generally accidental - despite what the stories may tell you, happens closer to home than children safely conceived within a clinic.
It occurs where men, generally, indulge in unprotected sex with multiple partners within a relatively small geographical field. The chances of these children meeting is high, the chances of this pattern being repeated through the generations higher still.
It mystifies me why this doesn't concern anybody, but donor conceived children, for whom sperm and egg donors are subjected to stringent testing and highly regulated, are.
I wonder if it is because for the middle class parent, they know there is more chance of their child encountering the donor conceived child in the future than the children of Steve from the pub who has seven children by different mothers and is only 22?
Or perhaps it is because the mother in the clinic is perceived to be making an active choice, while Steve is little more than an animal really and cannot be judged for his natural urges?
Either way, the refusal to criticise the numerous less than ideal situations children are born into every year while donor conceived children are subjected to much self-righteous head shaking fascinates me.