Is hate permitted? Is there a difference between hating the behavior of someone or the person himself?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

To have a pure creed, Muslims are required to hate disbelievers. This, in fact, constitutes the creed of al-Baraa (i.e. to hate disbelievers and to avoid helping them).
Allah Says (interpretation of meaning): {Indeed there has been an excellent example for you in Ibrâhim (Abraham) and those with him, when they said to their people: "Verily, we are free from you and whatever you worship besides Allâh, we have rejected you, and there has started between us and you, hostility and hatred for ever, until you believe in Allâh Alone," …} [60: 4].
Thus, it becomes clear that our father, the Prophet Ibrahim (Alaihi As-Salaam), and believers with him declared freedom from all obligations towards disbelievers and showed them hate.
Therefore, every Muslim is required to do and be so. In simple words, a Muslim has to hate disbelievers from the depths of his heart unless they embrace Islam and become true Muslims.
The Prophet (Sallallahu Alaihi wa Sallam) said: "The strongest bond of faith lies in loving and hating for Allah's sake" [ al-Bazzar ].
As for a Muslim, we - Muslims - are required to love him to the extent he demonstrates good and piety, and hate him and his disobedience and misdeeds likewise. Then, our love to him increases by his better obedience and good deeds.
Allah knows best.