Conservatives pay attention to the principle of  variety, and embrace inequality as a healthy and necessary  factor in societal development. Let us be clear. Conservatives are not insensitive to inequality! Rather, they embrace philosophies and strategies that offer a reasonable management of the reality. One of those strategies is called competition. Competition necessarily and predictably causes inequality ... not for the purpose of subjugation, humiliation or domination, but for the purpose of advancing excellence. To quote Russell Kirk. "For the preservation of a healthy diversity in any civilization, there  must survive orders and classes, differences in material condition, and  many sorts of inequality. The only true forms of equality are equality  at the Last Judgment and equality before a just court of law; all other  attempts at leveling must lead, at best, to social stagnation."  
The Utopian dream of social justice is just that; a dream. Of course we recognize that social justice is just code for the redistribution of wealth. Social Justice sounds like a great idea, but it's unsustainable, because it violates the law of productivity:
- People will be productive when properly      rewarded
- People will prosper in an environment that      fosters creative expression, productivity and autonomy
- People want to keep the proceeds of their      labor and the freedom to distribute it according to their self interests
- People will resist productivity when not      adequately rewarded
- People will resist productivity when rewarded      for another persons labor 
Humans are born unequal and die unequal. It is this reality of inequality that, in part, feeds the human need to seek significance. Those misguided individuals and organizations who seek to take earned resources from the productive members of our society and distribute those resources to the non productive members of that society are wrong on two levels: On the first level, redistribution is unsustainable. On the second level, there must be a system in place for redistribution, and that system, however noble the effort, will not and cannot be equitable in its organization, methodology or outcomes. 
Conservatives embrace  variety, accept the reality that inequality will always exist, and submit that"... attempts at leveling must lead, at best, to social stagnation."  Russell Kirk