To seriously answer your question...
Always a mistake in this thread.
...The Cat in the Hat is in our world, cause he interacts with real people.
They're not real people. Firstly, they're fictional characters, which makes them imaginary people. But setting that aside, I'm also inclined to believe that they are cartoon characters. I can't remember off the top of my head how many fingers they have, but if it's four that's a dead giveaway that they are cartoon characters and thereby inhabit the "cartooniverse". If they have five that's still no guarantee that they're not cartoon characters, as there are other indicators that they inhabit the cartooniverse. Like a cat that talks and drives a car and stuff. And the talking fish is also suspect.
Horton's world contains the Jungle of Nool, which isn't in our world, and the Who's live on a speck in Hortons World. Hence there are at least 3 worlds, potentially more!
Yes, at least three. We've actually identified 5 worlds - Horton's world, the Who's world (a.k.a. the "Whoniverse"), the dustspeck within the Whoniverse, the Cat in the Hat's world and our own. Three of these may or may not be the same world (i.e. the CitH may exist in our world, which exists on the dustspeck in the Whoniverse.)
Or maybe not.
My question, asked before and never properly answered by serious Tolkien people, so lets have a more creative answer.
Aragorn and the company are attacked by Wargs near the Moria Gate. The morning after the battle the bodies of the dead wargs have disappeared, leaving behind undamaged arrows expect for the one that caught on fire as it flew.
So, where did these magic wargs come from and why didn't Sauron have a whole army of them at Minas Tirith?
I have no idea. But I couldn't help but notice that you mentioned "serious Tolkien people".
I think you've got the wrong forum.