The Wikipedia page for destiny states:
Destiny, sometimes referred to as fate (from Latin fatum – destiny), is a predetermined course of events. It may be conceived as a predetermined future, whether in general or of an individual.
Both destiny and fate are usually used in a more religious or superstitious senses.
Originally, I thought of words like coincidental or happenstance but they kind of lack the absurdness of the situation.
For interpersonal relationships birds of a feather flock together is pretty spot-on, but also quite a mouthful.