B/C the Republican party has come to embrace white christian identity politics so much that its base has been narrowed to that demographic. The party has completely alienated those who identified as Republican on the basis of economic policy. If you aren't a gun toatin', Bible thumpin', illegal hatin' patriot, then I would imagine it'd be difficult to have any sense of belonging within the party. As the base erodes away, the party's commitment to the views of these white evangelical voters is being reinforced.
If you look at the major partisan issues over the last 2 years, its clear that its shaping the platform: Objections to the ACA (on the grounds of religious liberty), objections to SCOTUS marriage equality ruling, Ferguson and other similar incidents (accused "anti-cop thugs"), bills legalizing discrimination against gay customers, refusal to allow Syrian refugees into the country, illegal immigration. This list could go on for days.

I feel like I don't need to go into much detail as to why the views of this group are so problematic. I'll just say with regards to race, this group dismisses legit accusations of racism as "PC culture", while labeling attempts to fight discrimination as "reverse racism against whites". They do this because racism is so deeply ingrained in their views that they feel threatened by any attempt to correct racism or discrimination. Think about how much of a fuss was put up over the removal of the confederate flag. This is just one of countless examples about how threatened these people feel by revisions to their values and lifestyle, and when race is at the center of the issue, they mistakenly perceive what they are experiencing as racism.

So to answer your question, the type of (reverse) "racism" these Republicans accuse others of isn't actually racism at all. It's a reflex that occurs because addressing issues of race demands that they need to stop being assholes when they don't want to.