Don't buy into the Right narrative here. The context of the statement was a discussion about the empirical odds of an extreme right-wing candidate achieving higher elected office in the state. Cuomo was just describing their highly improbable chance at winning in the current political climate with the phrase "extreme conservatives have no place in New York," drawing on the state's decades of history and the far Right's continued losses here. The Right latched onto it as if he was taking a moral stance on the existence and acceptance of people who hold far Right views in the state, and are using that deliberate distortion to generate outrage and controversy. This should be a non-story.
The funny thing about your observation is that their is no major presence of "extreme right wing conservatism" left in the states. Sure, there are small pockets of people that are attracted to far right political philosophy, however, these people have no major public support in the USA, or anywhere else in the west. Cuomo is acting like Golden Dawn is about to set up shop in NYC and become a major force. The Tea Party, as much as the progressive and liberal media want to paint them as "Extreme conservatives" are actually closer to Ron Paul Libertarianism, or Lockean Classical Liberalism. Of course, presenting the tea party as if they all might wake up one day and put on a Swastika armband is a great way to discredit their populist beliefs that have widespread appeal outside of Liberal, costal pockets.
The bigger issue here is the history of the bourgeois, progressive lefts hostile cultural and political war against mid-western and southern working class white people. Every policy, weather social or economic shows a deep seated hatred by the left of the more traditional, conservative, christian whites in this country. Others have noted that the United States is effectively two countries, and i don't see any reason to continue to allow the left, who has more access to the media, and a much larger academic influence to continue their hostile war of cultural imperialism and displacement of these people. Secession is the best course of action at this point.
I would honestly love to hear who Mr.Cuomo considers to be a "right wing extremist" in New York. Donald Trump? I wonder if Cuomo realizes how utterly defeated conservative political thought is in the West. People who vote conservative probably only do so because they don't want to pay more taxes, their brains are still effectively Liberal though.