And what you said was incorrect. Under 1A, the only content which the FCC can ban outright is obscenity, defined as per the document I linked; see FCC v. Pacifica for context.
I also assert that the morality being enforced by the FCC [in a given time period] will fall in line with the morality of the rulers of [that time period]. That is a descriptive statement.
Which part am I wrong about?
> The FCC is allowed to enforce a certain morality.
As I said previously, the FCC is bound by the First Amendment. They do not have the power to restrict speech, whether on grounds of "morality" or otherwise.
Obscenity is not considered speech as far as 1A is concerned, so the FCC is able to ban it. I disagree with this categorization, but it is what it is.