Undoubtedly, it is a sign of great misguidance that people occupy themselves with slandering the Companions of the best of mankind, Prophet Muhammad (peace and blessings be upon him), or with arguing about the disputes that arose between them, instead of occupying themselves with doing that which will benefit them in both their worldly and spiritual affairs.

Imam At-Tahawi said: We love the Companions of the Messenger of Allah (peace and blessings be upon him), without exaggerating our love for any of them, nor do we disavow any of them. Indeed, we hate those who hate them, and we only mention them in good terms. Loving them is part of our religious commitment, faith, and ihsan(benevolence), and hating them is disbelief, hypocrisy, and wrongdoing.

Answering the question, Dr.Muhammad At-Turki, professor of Shari`ah at King Sa`ud University, stated,

The narration that Mu`awiyah is the one who initiated cursing `Ali ibn Abi Talib on the pulpit is by no means authentic. Mu`awiyah was a prominent Companion who knew and respected other Companions, so it cannot be believed that he ordered Muslims to do this.
Indeed, I would like to warn the questioner not to rely mainly on history books in these issues, because these books are full of unsound and fabricated stories. Experts in history admit this.
the stance of Ahl As-Sunnah on Mu`awiyah is the same as their view on other Companions (may Allah bless them all and be pleased with them). Mu`awiyah is one of them, and his companionship with the Prophet (peace and blessings be upon him) is firmly established. Hence, it is unlawful to derogate him, since he is a Companion. Whoever does so is on the verge of real danger in his religion and creed.
I should remind my dear questioner of what Imam Ahmad ibn Hanbal said when he heard a man disparaging Mu`awiyah and `Amr ibn Al-`Aas: “This man dares to talk about them because he has a corrupted heart. No one hates a Companion of the Prophet (peace and blessings be upon him), except those who have corrupted hearts.”
also, when Al-Hasan Al-Basri was asked about those who curse Mu`awiyah and `Abdullah ibn Az-Zubayr, he said, “May Allah curse those who curse them!”
You should warn others about the seriousness of this issue.

May Allah guide us all to the right path!