Is speech over amateur radio constitutionally protected?
Could I theoretically sue the FCC for the right to broadcast music on 20 meters, and have a chance of winning on free speech grounds?
You can certainly sue. I don't know enough about existing jurisprudence to comment on the likelihood of success.
If the FCC made a rule, at the direction of Congress, prohibiting political speech over amateur radio, would that be enforceable? What if the rule allowed promotion of party X but not party Y?
Of course not.
The entire concept of regulation of telecommunications is in some tension with the first amendment, but the fact that the judiciary has upheld such regulation does not imply that telecommunications are beyond the reach of the first amendment. Instead, it means that the first amendment permits the regulation. Other regulation could still be found impermissible under the first amendment, as regulation prohibiting political speech or likely would and regulation giving preferential treatment to certain political parties certainly would.