Terms have definitions.

Big picture, conservatism attempts to "preserve" something. So, for the term to have meaning, you must ascribe it to what it is trying to preserve. Arguing that today conservatism is trying to preserve society as it was in the Middle Ages makes no sense.

I am saying the term "modern conservatism" refers to a movement, that originated in response to the spread of socialism during the 1930s.

Americans saw what was happening in Europe with Communism and Fascism and saw elements of socialism in FDR's New Deal and they responded by developing a framework on which to "conserve" America's core beliefs. In that context, conservatism does make sense.

The opposite of conservatism is Progressivism. Progressivism believes societies evolve over time to become better through change. In reality, that has not turned out to be true. Fascism and Communism were "progressive" movements that did not turn out well for humans but persist to this day even as they were offered as solutions to poverty and violence.

Modernity is not conservative or progressive, it represents a collection of ideologies that were "modern" at their time but ideologically aligns closer with today's conservatives and their embrace of classical liberalism. The primary divide between Modernity and Conservatism today is the use of Judeo-Christian values as part of our nation's core beliefs. The key word here is values, not theology.

Because modernity influenced thought that led to classical liberalism, which then became the foundation of our societal contract, today's conservatives are people who want to preserve that contract, not the one that governed the Middle Ages.