Hot topic here and I thought I’d put in my two cents. Although I will not be pitting them against each other.
These two ships are some of the most popular in the fandom, and they are also the most at war with each other, more so than other ships (for example I don’t feel like SouMako vs MakoHaru shippers share the same animosity towards each other). A possible reason for this: before the arrival of Sousuke in the second season there was an odd number (although RinTori is a thing), and the two most obvious choices for Haru were either Makoto or Rin.
I think however, knowing whether someone ships RinHaru or MakoHaru can tell you a lot about them, and what they look for in romance or just their relationships with others.
The MakoHaru romance has a calm, relaxed, comfortable feel to it. One that comes with time. It has a sense of almost unbreakable security to it (like an old couple that’s been married for years). A fire that’s now a soft ember. The RinHaru romance however is intense and tumultuous. It is a rivalry, full of passion and excitement. Like that pair that can only fight, thinks they hate each other until they realize it’s opposite.
Maybe each person and their respective ship (RinHaru or MakoHaru) is drawn to what they represent. They are very much opposite romances, and perhaps that is the reason for the vicious disputes.