Well, they “cope” with it by resisting it in every way possible until its forced upon them. To them, “slowly” means “at a time after my personal interest on Earth is over.” In practice, the only change they can “cope” with is that which benefits the majority stakeholders (eg, tax cuts for the wealthy, Sessions’ investigation into discrimination upon white people).
I can’t think of any civil rights progress that would have happened at all, if conservatives had had the final say. This includes: ending slavery, popular vote for Senate seats (repealing the 17th Amendment is still a thing for them), female suffrage, integration of the military, Voters Rights Act, ending anti-“miscegenation” laws, ending mandatory prayer in schools, Equal Rights Amendment (they won that one), women in the military, women in combat roles, same-sex marriage.
Your distinction between “conservatives” and “reactionaries” just doesn’t help much. “Reactionaries” would seem to just be conservatives who happen to have lost the political argument and let events pass them by. A “conservative” would just be a reactionary who’s at rest (there being no civil rights to repeal, yet).
