It seems you want a word for someone refusing to engage in discussion, because they regard the subject as not open to debate. To dismiss out of hand is one option which has already been suggested, or more neutrally you might have to disengage from discussion.
In a similar vein I would suggest shut down debate.
I also detail how accusations of trolling were used as a justification for shutting down debates about community expectations ... — Bergstrom, Kelly. "'Don’t feed the troll': Shutting down debate about community expectations on Reddit.com".
First Monday, Volume 16, Number 8.
In this quote, it is alleged that users refused to engage in discussion about community expectations and instead just "called troll", which is similar to your example where people "call out racism/sexism" rather than engaging.
I helped shut down an abortion debate between two men because my uterus isn't up for their discussion. — Title of an article by Niamh Mcintyre. The Independent, 18 November 2014.
Here the writer states that she prevented, rather than engaged in, a debate, because she felt the participants lacked relevant standing.
If you want give a more specific reason for the disengagement, rather than just acknowledge that the it occurred, you might like play the race card, or equivalently play the sexism card.
Playing the race card is an idiomatic phrase that refers to exploitation of either racist or anti-racist attitudes by accusing others of racism. — Wikipedia entry for "Race card", as of 3 July 2015.
An example usage from the British press:
Disgraced former mayor Lutfur Rahman (pictured) is said to have played the race card to silence opponents - and his deputy today reiterated claims there is deep seated racism in the borough of Tower Hamlets, in east London. — "Vote rigging party is STILL playing the racism card: Day after mayor is forced out, deputy blames 'Islamophobia'". Daily Mail, 25 April 2015.
And one from the States:
Democrats won't be able to play the sexism card if Republicans pit former Hewlett-Packard CEO Carly Fiorina against Democrat Hillary Clinton, says John Sununu ... — "John Sununu: Carly vs. Hillary Would End Dems' Phony Cries of Sexism". Newsmax, 31 March 2015
Both of these news sources are notoriously conservative: I don't think either card-playing idiom is very likely to be used by a political liberal or centrist except ironically! So these are less neutral terms than "shutting down debate" is.
Perhaps dogmatic?
Merriam-Webster: "expressing personal opinions or beliefs as if they are certainly correct and cannot be doubted"
or, upon looking for synonyms for dogmatic, there's doctrinaire:
dictionary.com: "dogmatic about others' acceptance of one's ideas; fanatical: a doctrinaire preacher"
Best Answer
I'm not sure there is one word or phrase for such a person, although in some contexts the term independent covers a lot of idiosyncratic political views. And there is a class of people who call themselves "economically conservative but socially progressive/liberal", however there is no one word for this (fairly common) type.