If you equate evolution with competition between organisms to ascertain which is the fittest, conservatives ought to love it as they tend to believe competition is good and challenges each member to be his best. An evolutionless world would look to many American conservatives as the biological equivalent of the government: no real competition.
While conservatives in the US largely believe in competition between individuals, that is because conservatism is here associated with laisse-faire capitalism and hence preserving that social order unchanged is part of the conservative ideal here. However conservatism does not believe that such competition should lead to evolving social systems. Rather conservatism believes that society ought to be static in its social structure. Conservative dogma holds that if one were to take a random sample of people from 1014 and a second random sample of people from 2014, while each sample would have stronger and weaker individuals, then once controlled for the effects of a thousand years of technological development there would be no discernible differences between the two samples taken as a whole because the nature of man is unchanging. Conservatism holds that society should be without evolution and that our current society (or perhaps a past version, if one is a reactionary conservative) is the best possible one and that any deviation from it inevitably leads not to evolution, but to degeneracy.