The paradox of intolerance is a property of rules, and a recommendation on how to write them. It simply says that tolerance cannot be enforced absolutely; some intolerance is necessary to maintain tolerance.

It's the same idea as "If you wish for peace, prepare for war". Absolue peacfulness only allows the violent to perform violence easier, so some violence needs to be possible to maintain peace.

Lastly, intolerance isn't simply advocating for new rules. It's not intolerant to say you want to walk to work, or you wish education was free for everyone. Intolerance is an existential problem; "homeless people should not be tolerated in the city", "immigrants should not be tolerated in this country", "homosexuals should not exist". The paradox of intolerance says that these ideas should not be allowed to exist, and that permitting their existence directly threatens the existence of others.

Put into social contract terms; "Advocating for someone to be excluded from the contract is just breaking the contract with extra steps". Same idea, no paradox.