Hill v Colorado:
"Also, the statute deals not with restricting a speaker’s right to address a willing audience, but with protecting listeners from unwanted communication." - upheld
Regardless of context, I believe this US Supreme Court reasoning will carry across to protect parental rights. The FCC is already enforcing standards that are below the threshold of numerous complaints. I think what you will see is the requirement enforced that there must be a direct parental elective mechanism, so open airwaves broadcasting will be subject to legislation. Beyond that, a network may drop a program for personal reasons of an executive or simply to respond to the weight of complaints, avoiding the hassle and possible effect on more important business objectives.
Since moral standards are being continually tested these days by radio and television, the ubiquitous nature of this material will force cable companies to unbundle their channel offerings, allowing individuals to completely control what channels are available in their homes and to enable them to immediately exclude any one channel that presents a problem to them by their own standards. While channels may be able to be individually blocked, there may be a desire to withhold any form of funding for such content, i.e. not pay for any part of a subscription that isn't desired or used, in effect boycotting certain channels, reducing their undeserved funding.
The only way to overcome that is by the tyranny of the majority, still relying on networks to not care what image they project. To stand back and obstinately describe how things should be could be considered your own brand of tyranny.
This really is a no-brainer for responsible parents and others who care about wholesome child rearing environments. Adults can watch, hear, or otherwise experience anything they want to, as long as it is strictly in private and does no demonstrable harm to anyone else (and is otherwise lawful).