Comment 23 by Zeuglodon :

I have a simple word that could solve this problem. It's called "egalitarian". An egalitarian believes in equality, and that best describes our goals for the removal of religious privilege, while promoting secularism, equal (or human) rights, democracy and other such values.

That's a good word to use, but it needs modifying to something like "progressive egalitarian" or "elite egalitarian"... something that suggests we're not indulging in Tall Poppy Syndrome or Crab Bucket Syndrome.

Obviously there is a contradiction to associate elitism with egalitarianism, since they're complete opposites. My point was to try and use a simple word to describe the multifarious movements that generally make up our political and ethical positions.