3. New York Yankees
The Astros have knocked the big-spending Yankees out of the playoffs in three of the last six postseasons. The New York Yankees have never beaten them in a playoff series. All three series were competitive, but this rivalry stems more from off the field drama than anything else.
Aaron Judge publicly called the Astros cheaters, and was apparently sick to his stomach about it. The city of New York collectively hates the Astros for the sign stealing scandal, and chants slurs about Jose Altuve, even when they are playing other teams.
I don’t think this rivalry can move up in the list until the Yankees actually beat the Astros in the Playoffs, but it sits above the Dodgers and the Athletics simply because of how often the two clubs have faced off in the postseason in recent memory.