While there are notable exceptions on both sides, my impression is in general the tendency is for conservatives to focus on the issues in debates and arguments, whereas in general the tendency is for liberals to focus on individuals in debates and arguments. Generally speaking, conservatives tend to focus on debating the pros/cons or merits/demerits of an issue, whereas liberals tend to focus on the morality/immorality of an individual.
For example, if someone disagrees with tax hikes, then they hate the poor. If someone disagrees with abortion, then they hate women. If someone disagrees with Pres. Obama, then they hate African-Americans. If someone disagrees with illegal immigration and amnesty, then they hate Hispanics. If someone disagrees with same-sex marriage, then they hate homosexuals.
At its most crass, it's nothing short of bullying. Name-calling, insults, shaming.
Yet, ironically, this is not only exactly what Trump the supposed bona fide conservative engages in, but this is the address where Trump lives and thrives. Simply witness his performance in the latest GOP debate in South Carolina.