Should a tolerant society tolerate intolerance?

A case for

It could be argued that a tolerant society should tolerate intolerance, as difficult as that can be sometimes, as much of what is deemed as ‘intolerant’ is often just miseducation and misunderstanding in disguise. If a tolerant society were to deem themselves tolerant, they must do so in the form of treating everyone at the basis that they can change.

The first objection

You're confusing tolerance with naivety. Yes, people can change—but tolerance isn't a suicide pact. When "miseducation" calls for your elimination, you don't educate it into submission; you stop it before it stops you. The Weimar Republic tolerated the Nazis into power. Treating intolerance as just a misunderstanding you can reason with ignores that some ideologies actively exploit your tolerance to dismantle it. Real tolerance protects the tolerant from those who'd destroy tolerance itself. Why should your society risk everything on the assumption every intolerant person wants to be educated?