What constitutes an enemy of Islam/Allah, or a non believer. I always imagine our Prophets and Imams, our role models, being soft hearted, patient people. Yet we are instructed not to be apparenty? If you can shed light on this issue i'd greatly appreciate it.

It depends on the situation and environment
Sometimes Taqiyya needs to be practised to save life
Sometimes in a battlefield we need to fight
Other times we might need to use intellect wisely and act accordingly under advice of ulema.