Exactly. Different religions yet they overlap astonishingly well. Typically one God or Gods and they're given human-like features and they're creators and masters of the things around us. So regardless of where humans are found, we're bound to find their music overlap almost identically to our own if given enough time for their musical recordings to evolve. Music is just another function of the brain, an expressive feature of the human brain that enjoys certain notes and patterns.
It just seems to me that after ~100 years of recorded music, we've run the gamut and are out of ideas. There are no new music genres... hip-hop and EDM were the last musical developments and no new musical direction has been seen since... and both are now decades old. Why? Because we're bound to a limited array of notes that we find pleasing to our ears.
My guess is that our music is only "unique" insofar as the time and place in which it occurred. The when and where is happenstance, but on a statistical basis, humans on another planet are bound to cross the same musical threshold as us eventually. Their Beatles might not arrive in their 1960s but thousands of years earlier or later depending on how much focus is given to advancing their planet's recorded music catalogue.
On our own Earth, at any given time, there are people who can sing just as well as, and sound almost identical to the greatest singers of our past. They might not have access to recording technology, or might not have ever tried to sing, or might not be interested in singing, yet that latent ability is there. It's always present on Earth... just as you have doppelgangers on Earth at all times, the same goes for vocal chords. Ditto for musicians... there is another person who can play guitar like Eddie Van Halen out there right now but his hands have never touched a guitar. For that matter, there is another person with the skillset of Beethoven out there somewhere. But over millennia, through the eclipse of time, these things would coalesce and those other humans on that other planet would have comparative music to our own. It's inescapable. We are not special nor is our musical heritage. We're just doing what humans are destined to do.