If I recall correctly the anterior cingulate cortex is what activates when detecting negative social evaluation and regulating affect. One theory is that certain cultures (more common in the Southern United States than Northern, studies like this suggest: https://www.ncbi.nlm.nih.gov/pubmed/8656339/) instill responses that present increased symptoms of anxiety, aggression, or stress to what might be taken as threats against one's "manhood".

Now I'm not saying all Republicans simply have problems regulating their emotions, but I am saying that it is common in many cultures for men to have responses of fear to cognitions that indicate they are not "manly", and that the connotation or perception of the concept "manly", which implies essentialism about gender, varies quite a lot across cultures, while the physiological behaviors or affective states associated with "being manly" are correlated with many different biological functions. That often become "machismo" when the expression of "manliness" is taken beyond having any socially acceptable or rational function in culture or morality, and examples could include getting into fights over sports teams. Trump, like Putin, or even President Duterte of the Philippines express and illicit in their supporters machismo, and, I gather from my own experiences with the types of people who support Trump that much of the force behind his supporters do so out of fear of "being emasculated".

Is this the counterpoint to Democrats welcoming emasculation?

Spokes as if the connotation (the most generous one I can think of to explain how Democrats might be emasculated) of "being a man" was something that could be taken away in a discussion. This is definitely the kind of response I would expect, but of course we are only exchanging comments in a thread and I couldn't make any worthwhile generalizations.