Does one fall into disbelief if one hates the Companion Mu'awiya—may Allah be pleased with him—based on what one has read about his actions, and then decides not to hate him personally but rather to hate his bad deeds?

What happened is not disbelief (kufr). We advise you to avoid obsessive thoughts regarding this matter. The creed concerning the Companions and the disputes that occurred between them is explained in many fatwas. To understand the virtues of Mu'awiyah, his deservingness of the caliphate, and the praise of the Companions for him, one can refer to Fatwa No. 127506. What transpired from Amir al-Mu'minin Mu'awiyah (may Allah be pleased with him) that was censured was, in general, a matter of ijtihad (independent reasoning) for which he is rewarded either once or twice. We advise reviewing what has been written in his defense and clarifying his interpretation regarding what was censured, such as Shaykh Ali Al-Sallabi's book on the Umayyad state.