I think the issue with conservative/right-wing groups (which, in effect, also means mostly white and religious as well) complaining about being discriminated against is that it just doesn't effect them in such a powerfully negative way as it does someone in a minority segment of the population, who's upward mobility in society (not to mention physical and mental health) is harmed on a much bigger scale. If you're a christian republican, you can deal with stress and discrimination against you by simply moving to the christian republican part of town and, unless we're talking about the deep rural south,it will usually be a comforting place that looks nice, has very little crime, and serves as an opportunity for you to seclude yourself in a comfortable room far away from those horrible minority groups who were mean to you. This form of escape is seldom available to minorities. If you are black, atheist, gay, jewish, or whatever, you still have to get up every day and face a world that requires the burden of conformity to some degree in order to be successful. If you're gay, yeah you can move to a gay part of town and will probably have the opportunity to be happier in an emotional and material sense, but believe it or not most gay people (for example), don't like only being around other gay people. Most minority groups in fact would rather be in a diverse environment. And if you're black or hispanic, there's a much higher chance that you don't have any sort of luxuriant place where you can escape the stressful experience of conforming to whiteness.
I just feel like the religious conservative right have a vision of the world in which everyone needs to conform to their beliefs: talk white, be a good church-going person whether you believe in a god or not, etc. Where working hard is all anyone ever needs to do to be successful, despite the fact that such a philosophy is much, much more effective if you happen to be white conservative. I know not all conservatives are white. As we saw at the RNC, there are at least a good 5 or 6 minorities and they aren't all necessarily unhappy conformists. I like Michael Steele a LOT, though the majority of his party doesn't seem to feel that way.
So that's why I can't really sympathize with conservatives when they complain about discrimination against them. Oh no, an oversensitive black or gay was mean to you. Go back to your family in your suburbs and get the fuck over it.
EDIT: that said, I will say that the poster child for the kind of liberal being discussed in that article is Bill Maher, and he is most definitely a raging asshole towards towards conservatives. Probably more than anyone needs to be.