Why is it impermissible for a Hanafi to shake hands with a Shafi'i?

The Hanafis, Shafi'is, Malikis, and Hanbalis all follow the Prophet, peace and blessings be upon him. They are schools of jurisprudence (fiqh) dedicated to deriving rulings, and their ultimate goal is one. If there are bigots who cling to one madhhab and show hostility towards those who follow a different one, this is attributed to ignorance, extremism, and blameworthy fanaticism, not to the madhhabs themselves. All jurisprudential madhhabs are sound and valid, and their followers are brothers who pray behind a single imam, facing a single qibla, and derive their guidance from the Book of Allah and the Sunnah of His Messenger. Whoever believes otherwise is ignorant.