The Republican Party are distinct from the concept of conservative and reactionary politics. They practice both. As do the Democratic Party for that matter.

https://en.wikipedia.org/wiki/Conservatism

https://en.m.wikipedia.org/wiki/Reactionary

(See also https://en.m.wikipedia.org/wiki/Progressivism)

It's useful to tease these concepts apart so we can better understand & critique certain policy positions. When Democrats vocally oppose student loan forgiveness, they are practicing conservative politics, for instance. It's not simply that Republicans are reliably conservative and Democrats are reliably progressive.

And there are many other forms of politics, these are just the most prevalent in US politics today.