It is related because the government does not do one thing. Or anything well for that matter. Not that they don't try and in the process stretch their mandate far beyond what was originally specified: "These interests are wide-ranging, including consumer protection in commercial contexts; the development of technological tools to empower users; and speech and democratic participation". So please tell me why you need a government "net neutrality" commission to ensure your "democratic participation" unless somehow you can't post here anymore because your ISP only allows their own brand of forum and not FreeRepublic.
Yes, if the government engages in constitutional regulation of interstate commerce (net neutrality), it perfectly follows that the government will use that in order to quell free speech. You have presented the worst slippery slopes I have ever seen to try to connect net neutrality with other issues.