The wiki states that tamed cats will not teleport to the player if in another dimension. They will stay in their dimension until the player returns.

Perhaps I have misunderstood, but I took this to mean that cats will not follow you into the Nether, or the End.

Today I traveled to the nearest jungle biome on the server I play on, which is hosted on Realms. This is roughly 25,000 blocks away from my home, but luckily we have a portal network set up. I planned to have a friend wait at the jungle after I tamed my cats to keep the chunk loaded while I ran back home through the Nether, causing them to safely teleport to me once I reached home.

They followed me through the portal, however, as did my parrots. The cats unfortunately did not make it home with me, as they teleported into some lava when we were almost home.

Attached is a screenshot showing myself with my parrots and a cat in the Nether.