Imam Hasan (AS) did not do Bayt of Muawiya, infact it was a treaty and though it avoided blodshed for the time being, it led to Muwayia to violate the treaty and installed his son Yazid (LA) as the ruler over Muslims. Yazid (LA) in turn was responsible to shed the blood of the nawasa-e-rasool Imam Hussain (AS) and his family and friends within a period of 50 years of wisal of Rasool Allah (SAW)
Although I am against abusing anybody specially Sahaba, we need to distinguish between those truly loyal to Allah and His Prophet (SAW) and those who violated Allah's Shariah and Sunnat-e-Mohammadi (SAW). Unfortunately Muwayia was one of them.
You should not compare. One was the nawasa-e-Rasool Allah (SAW) who was called the sardar of the youth in Paradise and gave his life so the lines between right and wrong are clearly marked for all the times to come. The other one on the hand was the son of a known enemy of Islam and the Prophet (SAW), whose mother ate the Liver of Hazrat Hamza uncle of the Prophet (SAW). He was responsible for killing Sahabi Hujr Bin Adi (RA) along with his companions since Hujr refuse to curse Ali (AS).
Just a few more additions to the points mentioned by bro righteous:
1) Yazid did what he did to the family of the Prophet; his other hideous crimes included battle of Harra, where many companions of the Prophet (saww) were butchered in Madina, their property looted and their women violated. In Mecca, among other crimes, his army hurled stones and wood at the kaaba and set it on fire.
2) The books of history contain names of more than 120,000 people who are all identified and counted as the Ashaab of the Prophet (saww). This list contains all types and degrees of people, including the hypocrites.
3) For "hisbuna kitaab Allah" group: Imam Hasan (as) is part of at least three very clear verses in the Holy Quran; verse of purification, Mubahila, and Muwaadat.