Star Trek gave us a future to shoot for. Lenoard Nimoy just acted in the TV Show. Gene Roddenberry had an optimistic future about Humanity, that really, we could all get along with each other, and use science, reason, and education to solve our problems. There are a few notable flaws with this way of thinking.
Where are the Christians, Jews, Muslims, Hindu, Sikhs, Jains, etc etc. The answer is: They don't exist. In the universe of Star Trek, there are no gods, only creatures we don't understand. Some friendly, some hostile we must overcome by intellect or force. All Humans in Star Trek are a kind of Secular Agnostic Deist. Nobody fights wars over the stuff we fight over because we are seen of one of Billions of Species spread all over this universe in a vast cosmos. This would result in social upheaval, mass hysteria, and suicides, and homicides at first as there are people so indoctrinated in these cults, that the shattering shift in reality would be unreal.
Another thing that makes the Star Trek Universe "Possible" we don't have is Matter Replication and Transmutation. We know enough to take any given source atoms and convert them to any given destination atoms with minimal effort. All thats needed is electricity to power the machines. This would result in the collapse of Capitalism as we know it. A kind of Socialism would take its place.
The last thing that would make Roddenberry's Future possible is Anti-matter Fusion and Fission. This would provide us with nearly limitless power generation capabilities. Its also extremely dangerous and can lead to a large scale ka-boom
Earth's Government in Star Trek is a unified secular government with a guaranteed Charter of rights. All three Abrahamic religions would flip their shit. As a government like this is described as being despised by the religions as a sign of the Apocalypse. The reason is with with a "Government of Planet Earth and all Terran Colonies" all laws would need to be based in reason and have a rational justification for existing and secular purpose. Equality and Egalitarianism would be necessary for this to work, and the Majority of religions are completely contrary to this concept. So, basically, for a Future like Star Trek to work, the heritage of our ancestors has to die.