At this point most of the Republican Party is reactionary rather than conservative.
Conservatives can cope with progressive change, they just want it to happen slowly. Reactionaries want any change do be undone and things put back to “how they were”*, see groups like the neo-confederates as an example .
* “how they were” doesn’t have to bear any resemblance to history.
I don’t know about the US, but at that time in the UK some of the older conservatives were practically socialist in comparison to Maggie Thatcher and (later) Tony Blair.
