Without science we would still think that the Earth was at the centre of the Solar System and the World was flat and now it has come up trumps again by showing us how to shut up a big mouth right winger in an argument.
The secret, according to Robb Willer who is a professor of sociology and psychology at Stanford University, is to not bombard the opposition with facts and figures but to frame your argument in ways they understand which is to frame it in a way which resonates with their world view which means appealing to the firmly held right wing view of 'respect for authority'.
If you can somehow show that an ideal or person shows a lack of respect for authority then it will soften the right wingers view, not enough to get them to change their mind but enough to at least let you put your side for the argument across.
A current example is Donald Trump who appears to be much loved by the right, hated by the left, but if the argument is prefaced by the idea that he repeatedly behaved disloyally towards America to serve his own interests by dodging the Vietnam draft to follow his father into the development business, then you will receive a more sympathetic hearing from your opponent as you are directly playing into their 'disloyal to me and my country' alarm zone which will temper any following good things they feel about him.
This can be doubled up by making the right winger believe that they have reached the conclusion by themselves, then they will be putty in your hands.
An example is while debating with a racist, sexist or homophobe and nudging them into thinking they reached a conclusion themselves, so when the racists says something along the lines of 'all blacks are evil' ask the racist to recall a time when they were on the end of discrimination at school or at work because they were different and how you are fighting to change attitudes to end discrimination at work or school so they others would not have to ever feel like they did again.
Somewhere inside that right wing head something should chime while thinking about their own experience and how others wrongly pre-judged or discriminated against them should lessen their own prejudices against others they consider different.
The professor also explains how to frame an argument to appeal to a left winger and sway or at least temper their argument but as a left winger myself we don't need to go there as we are never wrong anyway so i never read that bit.