Edit: I have an example. Have you heard of the so-called "Letter from the Eight White Clergymen" aka "A Call for Unity"?
Some would classify the authors of that letter as conservatives, others as liberal reformists (as opposed to revolutionaries). But the ones who wanted to keep racial segregation and Jim Crow laws alive at the time, were, without a doubt, the social conservatives of their day.
(sorry for using an American example, I hope you realize what I'm referring to).