This is incredibly hyperbolic and misleading. The Communications Act of 1934 was passed for a variety of very necessary reasons at the time, the most important being making sure broadcasters didn't hijack each other's signals.

Coughlin's show coincided with the creation of the FCC and they never really tangled. His show was pulled off the network a full 5 years after the FCC was established. FCC regulation may have had a part in that, but there is no reason to believe he in particular was targeted and certainly not that the law was passed to target him.

In an amusingly bald bit of Wikipedia editorializing, while the Coughlin page links to the Communications Act page in the context of (as the upthread throwaway account[1] says) half-implying that it was created to censor opinions...

...the actual page linked doesn't mention Coughlin at all: https://en.wikipedia.org/wiki/Communications_Act_of_1934

[1] The habit of throwing discussion bombs like this from throwaway accounts is another sign of HN's decay.