This exact question was answered by one of the Mario creators actually.

GAME INFORMER: Time and again, Bowser kidnaps Peach. Why do Mario and Peach still race go-karts and play tennis with him?

SHIGERU MIYAMOTO: If you're familiar with things like Popeye and some of the old comic characters, you would oftentimes see this cast of characters that takes on different roles depending on the comic or cartoon. They might be businessman in one [cartoon] or a pirate in another. Depending on the story that was being told, they would change roles. So, to a certain degree, I look at our characters in a similar way and feel that they can take on different roles in different games. It's more like they're one big family, or maybe a troupe of actors.

Not really a fun lore answer but it is the "real" answer.

https://www.gamedeveloper.com/design/mario-storytelling-as-theater