I disagree with your friend. Using cartoonish humor to mildly mock a candidate is a survival mechanism (I collect those nicknames: ex. Benedict Donald, Mango Mussolini, Trumplethinskin). It’s “punching up.” He is not put in danger by the nicknames.
There is no comparison to the “punching down” dehumanizing ways he refers to people. For example, attacks on Asians increased each time he used the “Kung Flu” slur. His Muslim ban contributed to getting Muslims and people his ignorant followers “thought” were Muslims (like S. Indian Sikhs) killed. Calling migrants “vermin” echoes language that led to the Holocaust.
No comparison.