Much of "social justice warrior" discourse is just rhetoric with the aim of getting the other person to shut up. The content is not the point -- there doesn't necessarily have to be any content -- the point is to shut the other person up.
For example, the idea that men should defer to women on "women's issues" and shouldn't talk about them. Whatever justification is given for this (e.g. "privilege") doesn't matter; the result is "shut up".
An effective defence against this technique is to point it out.
Such people often aren't reasoning with. Anyone who explicitly wants you to shut up certainly isn't. They have shown they are not open to reason.
Your aim with continuing speech (not shutting up) is not to speak to the person trying to shut you up, but to bypass them and speak to everyone else.
People who want to shut you up are not getting rid of you, they are just creating a parallel society which they are not part of. The same goes for people who want to deny you free speech, "no platformers" etc. This is not to deny that they pose a threat, but the response to that threat cannot be to reason with them; it must be to bypass them.