At the first look the new upcoming IETF standard HTTP2 has nothing to do with the right of free speech. Even a closer look at the current internet draft shows that it still has a "unsecure" HTTP mode as well as a TLS secured HTTPS mode. However browser vendors like Google or Mozilla announced that they will only implement the TLS secure mode and not the unsecure mode. See for example Poul-Henning Kamp's HTTP/2.0 article on more complaints about this.
Secure mode has a number of advantages including that it makes it for NSA, FBI or whoever harder to listen what you are saying. To enable the client that it really talks to the given server the server need to present a certificate signed by a certificate authority (CA) known by the browser. Again this is a good thing as nobody should speek in your name. Now there is also a disadvantage in this. Such a certificate can be revoked by the CA. Some goverments may be able to force some CAs to revoke a specific certificate they signed. If this happens then suddenly your speech become unavailable to all clients which use certificate revocation lists or the Online Certificate Status Protocol (OCSP) to check the certificate validity with the CA. This happens world wide regardless on how many servers have a copy of the content or where the servers are placed. In future this may be built into more protocols as the Internet Architecture Board (IAB) published it's strategy in a "Statement on Internet Confidentiality".