Your definitions of unacceptable speech & legitimate threat are unclear, and people nowadays make claims loosely. If it means demonstrable harm, then they’re fine & I apologize for the excessive caution.

From context

Rawls emphasizes that the liberties of the intolerant should be constrained only insofar as they demonstrably affect the liberties

and key words

only when the tolerant sincerely and with reason believe

and my direct statement

speaking one’s mind is not an act that directly & demonstrably harms/threatens security or liberty

I’m stating reasons of demonstrable harm are largely absent in speech. Speaking one’s mind doesn’t cause harm. Harm requires an act.

Tolerance is the allowance of objectionable (expression of) ideas & acts. That objectionable acts directly & demonstrably harm/threaten security or liberty is an easier claim that fits Rawl’s conclusion consistently. That speech alone can do so is a more difficult claim: maybe only false warnings or malicious instructions that lead to injuries or loss of rights, coercive threats, or defamation.