They can be potentially harmful ... or also possibly beneficial ...
Stress and hormones
There's a reason why hormones exist and they do serve a function and purpose.
With seven years of study and practical application helping people and striving myself to achieve fitness goals, I have come to know a bit about stress and its effects on the body and brain. I claim no knowledge on this topic beyond what is stated above, but I am confident in saying the kind of stress produced by despising something is in no way beneficial to any human being.
That kind of stress is not a cause. It is a result. It comes after people consciously decide or unconsciously develop the mindset to despise something. The thoughts produce the emotional response. And part of that response is the release of harmful stress hormones into the bloodstream.
As you correctly say, stress can be beneficial, like when you are in immediate danger (like in a burning building) and the fight or flight response kicks in; or when you are on a foot-race starting line or weightlifting platform about to attempt a performance level you have not previously topped. But that is beneficial only until the event passes, and once it's done, you calm down.
Those are different applications of stress than that produced by despising someone or something. The stress that comes from despising is chronic and exposes the person maintaining to several health risks.
In other words, if you spend time despising a political opponent or idea, you are boxing yourself into a limiting point of view that blinds you to other possibilities. And you are injecting hormones into your body and brain that can degrade your health and happiness.