Communism is when society becomes so technologically advanced and so abundant in resources that the state withers away and currency is no longer needed.

Okay, so not Star Trek then as there is explicitly a state. The Federation itself has its own mandates and laws but every individual planet is governed as well. The Federation is a Representative Republic that has an election every 4 years.

Also, his wife said he was a Communist

Actions speak louder than words and his actions blatantly demonstrate that he was not a communist.

Roddenberry, fearing that he would not make money off of Trek, wrote lyrics to the song, without any intention of using them, to get half the royalties—money that should have gone to Courage. Courage was so furious that he never returned to work on Star Trek (Deezen). Roddenberry, unapologetic, continued to see more and more profits from the franchise, becoming very wealthy over the years. The irony is that Roddenberry identified as a communist, according to his wife Majel Barrett-Roddenberry (Bennett). One would expect someone who identified as a communist, a bold label to adopt during the Cold War, to go to greater lengths to avoid such a serious income gap between himself and his employees.

Source.

Currency was even a thing during TOS, something that often gets ignored. Federation Credits. Credits which were used to entice bounty hunters to go after specific targets, to purchase highly unique items and used to pay for the training of crewmen. Kirk bitches about how much it costs to train Spock at one point. Kirk even gave Scotty ‘a weeks bonus pay’ for getting the phasers up and running when dealing with the Doomsday machine. Think all that ended in TOS? Well, no. Federation Credits were still used constantly in TNG. The Barzans and their wormhole. The Federation was willing to cough up over a million credits then and there plus another 100k every year after that to get rights to the wormhole. More examples on top of that that are not exactly difficult to find.

Nothing about Trek is ‘communist’ and it’s often wildly misunderstood to be so. Very little about Gene was communist other than a claim from his wife after the man had died. And something that he never really demonstrated at any point in his life.