No, free speech (and the related freedoms of press, religion, and association) is a cultural value that says every member of society should be free to choose which ideas they will promote and which people they will associate with, applying their own values.
That absolutely includes choosing which ideas from other people they will participate in spreading, which, yes, is censorship (but not public censorship), but remains absolutely central to the ideal of free speech.
Freedom of speech is not entitlement to have others cooperate in spreading your speech.