In so far as he is an apostle, the Catholic is a counter-revolutionary.
But he can be one in different ways.

A sample of the various campaigns that the TFP have been doing over the years. Click to see what you can do to be a Counter-Revolutionary!
Plinio Corrêa de Oliveira, Revolution and Counter-Revolution (York, Penn.: The American Society for the Defense of Tradition, Family, and Property, 1993), Part II, Chapter XII, pg. 118.