What is the meaning of the fiqh maxim that disputed matters are not censured and only matters of consensus are censured, and how is it applied?

Summary

Matters of valid scholarly disagreement should not be forbidden by hand (authority), tongue or heart in the way that wrongdoing agreed upon by scholars is. The disagreement must be a recognised one, supported by strong evidence and sound reasoning. Such matters may still be debated academically among qualified people, and a person who finds one view clearly correct should follow it but not stop others from following a different view. Al-Suyuti lists exceptions: a position with a very weak basis, a case brought before a judge who rules by his own school, and a case where the one objecting has a right over the other person.

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