When the Cat embarks on Project Emergency Clean-Up with his (big, red) clean-up machine, the books he returns to the shelves are pink.
Remember the word "pinko"? It was used to describe people who were sympathetic to the Communist Party. Could it be that the kids' mother is already a Communist, or at least a sympathizer? Meeting the Cat might just be part of the kids' training for the cause. In fact, it makes us wonder if the mother actually sent the Cat to the house to begin with. (Check out her "Character Analysis" for more on that.)
In the end, Seuss doesn't seem to be making any statement about Communism here, but rather venting, exploring, and seeing what he can get away with. There's too much ambiguity to pin him down, and we bet that's just how Seuss wanted it.