Why don't my tamed cats teleport to me?

This might have something to do with the server render distance/your render distance. If the render distance on the server/client is too low, then it's likely that the cats won't teleport to you.

The cats might also be sitting. Right-click on them to make them not sit and (hopefully, if your server/client isn't just plain broken) teleport to you when you get far enough away.

Also, if you'd like your pets to go through a nether portal, you should have them stand in the portal fluid to teleport them there, then you got there, then you're all in the nether by your portal!

Unloaded chunks can cause pets to freeze. This is what happens when your render distance is set too low. If you'd like your pets to teleport to you while you're in the nether, have someone stand close enough to your pets to have their chunk rendered so they are able to teleport to you.

From what you wrote, it seems like you don't have problems with cats in the overworld teleporting to you while you're in the overworld, or cats in the Nether teleporting to you when you're in the Nether. What you're expecting seems to be cats teleporting from the overworld to the Nether or vice versa.

Well, it doesn't work, never did, not with cats, not with dogs or other pets. They have no clue how Nether portal works and don't have the ability to teleport across dimensions on their own. When you cross into the Nether, the cat in the overworld will sit down and stop moving until you return to the overworld - it can't find your location and teleport or walk to it if you're in a different dimension.

What you can do instead, is to seat the cat next to the portal (on a block level with the portal so you don't have to push it "uphill" and nudge it into the portal. The cat will teleport to the Nether, and you can follow into the Nether - the cat will likely be sitting inside the portal. Rightclick it to make it stand up, and walk to wherever the exit portal is, then repeat the procedure of pushing the sitting cat into the portal there.

Note you must wait at least 30 seconds between the moment the pet exits the portal (definitely, fully walks out of the frame, not just 'moment of arrival' or slides to the edge of obsidian) and the moment it can be send through a portal again (the same or another). Otherwise it will just won't get teleported to the other dimension.