Lucy’s grandfather was a communist and she joined the communist party as a young woman because of him.
There was a big brouhaha when that info came out during the McCarthy era. But everyone Loved Lucy and it blew over.
Especially because Desi’s father had to leave Cuba because he was being persecuted by the Cuban communists.
It was because J. Edgar Hoover loved Lucy. He would clear his daily calendar so he could watch "I Love Lucy" at home. He offered Desi Arnaz a way out if he would play ball, which he did.
In a warmup to the show's audience, Desi said, "The only part of Lucy that's red is her hair -- and not all of that is really red." He got a massive laugh out of that.
It worked.