Is it proper to declare someone a disbeliever because of a difference of opinion, and what rules does Islamic law set for takfir?

Summary

Declaring others disbelievers is treated very seriously in Islamic law and should not be done recklessly against an individual Muslim. The ruling gives three principles: whoever refuses to deem a disbeliever by scriptural evidence to be a disbeliever may err in belief, whoever wrongly accuses a non-disbeliever of disbelief has the charge return upon himself, and wrongly leaving a disbeliever alone is a lighter error than wrongly declaring a Muslim a disbeliever. Scholars distinguish general takfir, aimed at an act or teaching, from takfir of a named individual, which requires investigation, questioning and establishing proof until no doubt or excuse remains.

Written in our own words from the original fatwa — check the source before acting on it.