Can a democratic socialist candidate truthfully take the oath of office?

Treasury Secretary Scott Bessent stated in a Fox News interview with Sean Hannity that Democratic socialism has become the center of gravity for the Democratic Party, echoing President Trump's predictions. Meanwhile, separate arguments suggest that the political platform of the Democratic Socialists of America contradicts the U.S. Constitution. This perceived conflict leads to the claim that members of the organization cannot truthfully take the oath of office required for public service in the United States.