Palpatine clearly says “the life force of your bond… a dyad in the Force” so it’s not something they were born with, but a connection that grows within them. So it doesn’t contradict Rey being a nobody, if anything it would strenghten that point if a nobody could develop such strong connection in the Force. And I also don’t see Snoke bridging their minds as a contradiction, but rather a step towards such a strong connection developing. Maybe it would help if Kylo said “What Palpatine doesn’t know is we’ve become a dyad in the Force, two that are one”.
It’s still clearly something that you would have to be born with. Otherwise, why wouldn’t the brotherly bond between Anakin and Obi-Wan be considered a dyad? Or between any Jedi/Sith pairing in general?
EDIT: Already know what your response is. Yes, Snoke bridging minds might cause the dyad to form, but then why hasn’t that been done before? It’s just a massive plot hole across the saga. Furthermore, Kylo says that the effort to project like that would kill. If it kills Luke, then why doesn’t it kill Snoke? This suggests that he is utilizing something that has always been present.