Can the state constitutionally require a private conversation?

When I originally posted about an article that Jennifer Brown and I wrote on Alternet, I received responses worried that it was dangerous to require the public disclosure of membership in unpopular organizations.

But the key to our proposal was to require a wholly private conversation between a discriminatory organization and it's potential members. As I explain in more detail in this Lessig post:

New Jersey might pass a new statute that mandates a private conversation
between organizations that wish to retain the right to discriminate and their
potential members. The organization would have to privately disclose to
potential members that it discriminates AND members would have to privately sign
an acknowledgement (which would be kept on file by the organization for the
possibility of in camera court review) that they wish to associate with an
organization that retains the right to discriminate.