Mu'awiya ibn Abi Sufyan spent most of his life with his father as a staunch enemy of the Prophet Muhammad (SAWA) till the victory of the Proohet over the Mushriks of Makkah when Mushriks had no choice but to surrender to the Prophet. Mu'awiya was an open enemy of Imam Ali (AS) and he was cursing him on the pulpits. He killed Imam Hasan (AS) by poison and killed Amar ibn Yasir in Siffeen battle with many other pious companions of the Prophet (SAWA). Sunni books narrated a prophetic Hadeeth that Mu'awiya will die as non Muslim ( Ju'nat Al-Attar by Al-Ghimaari 2; 145 and Majma' Al-Zawaa'id 5;243, and Shaikh Al-Madheera by Shaikh Abu Rayyah  185.

Those who love Mu'awiya are either unaware of his crimes because they were been misinformed. They need to read more to know what the Prophet (SAWA) said about Mu'awiya and what did Mu'awiya commit. Those who know what the Prophet said and what Mu'awiya has committed should never respect him because he was against Imam Ali (AS) which means that he was against the Prophet (SAWA) and against Allah (SWT). 

We don't call Nasibi but to the person who openly goes against Ahlul Bayt (AS).

'Wassalam.