Brain physiology is such that we feel good when we help others. The Golden Rule, treating others as we would be treated, is hard wired into our physical makeup. However, Mohammed attacked each and every neighbor. Attacking your neighbors is not an expression of the Golden Rule. But, there is no Golden Rule in Islam.
A Kafir is worse than an animal and is hated by Allah. Twelve verses in the Koran say that a Muslim can be friendly to a Kafir, but should never be a true friend. Sympathy allows us to put ourselves in the place of others. This sympathy is outside of Islamic doctrine. In Islamic doctrine those Muslims who are true friends with a Kafir are not truly Islamic.
My personal opinion is that this lack of sympathy for Kafirs is the worst part of Islam. The Koran places barriers between Muslims and Kafir, which violates the idea of humanity being of one spirit.