I know that there was censorship of horror comics through the 1950s-1970s, but a great deal of that seems to have been codified with the expectation that comics were especially attractive to (vulnerable/potentially delinquent) youth due to their format, on top of their distasteful content.

To deal with this briefly: pulp magazines faced little formal censorship from outside bodies in the United States, with the exception of the U. S. Postal Service which restricted the mailing of "obscene" materials; individual publishers had their own internal codes for content that they would publish in the magazines, from the generally sedate material of the the Argosy and Cowboy Stories to the sadistic covers of the shudder pulps and the spicy pulps—which promised steak but sold sizzle. The pulp publishers were the direct antecedents of comic book publishing, and early comic publishers had their own internal codes for what was and was not acceptable. However, just as their were shudder pulps, so too were their crime and horror comics that pushed the edge of acceptability; this came to a crux in 1954 when Dr. Frederic Wertham published his book Seduction of the Innocent and the shift in focus of the Senate Subcommittee on Juvenile Deliquency (with Wertham as the star witness); the major comics publishers then voluntarily joined together to create the Comics Code Authority as a form of self-censorship, to avoid possible government censorship on comics. This effectively killed horror and crime comics in the United States for a generation, although standards began to be relaxed in the 70s and 80s as companies and individual creators either ignored the CCA or worked around their restrictions.

I say this as a precursor because while there was a moral panic about comic books in the 1950s, it was focused pretty exclusively around juvenile delinquency, and particular genres of comics in particular (and therein lies a tale). It wasn't that comic books weren't read by adults, but it was a genuine "think of the children!" moment.

Did 20th century (1930s-1970s) horror radio ever face moral condemnation like horror comics did?

There were a couple outbreaks of outrage, but they were mainly very small and localized. The most infamous and long-lasting was the 30 October 1938 broadcast of The War of the Worlds, for more on which I strongly recommend Gosling's Waging The War of the Worlds: A History of the 1938 Radio Broadcast and Resulting Panic, the extant of which was sensationalized in the press out of proportion to how many it actually affected.

Part of the difference between comics and radio, however, is that radio already had the threat of censorship hanging over it in the form of a regulatory body: the Federal Communications Commission (1934, and before that the Federal Radio Commission, founded in 1926, and before that the Secretary of Commerce and Labor, given the power in 1912). Terror on the Air!: Horror Radio in America, 1931–1952 relates that, like pulps and comic books, individual broadcasters would self-censor their material to avoid offense out of fear of regulatory oversight from the FCC. The nearest equivalent to the Comics Code Authority for radio was the National Association of Broadcasters, who had an ethical code on broadcasting. It's hard to say how far this impacted horror radio shows, however.

The one really good example I know of is covered by Krutnik in Therapeutic Horror? Olga Druce, House of Mystery and the Controversy over Children's Radio Thrillers, which focuses on a 1945 case specifically looking at criticism over horror radio show aimed at a child audience - some clear parallels to the later comic book juvenile delinquency panic, and good reading.

Did horror radio have fan communities or enthusiastic fans in the same way horror comics/horror literature in print did?

Exact details are kind of vague and difficult to get ahold of these days, but there was some overlap between horror/mystery radio fandom and the fan-organizations which are the precursor to what we think of fandom today. Most of the time when you think of radio fandom you think of the organized fan clubs for Little Orphan Annie (remember the decoder ring in A Christmas Story?) or Captain Midnight--pulp and comic characters that made the jump to radio often had crossover audience with the existing print fandom (and the same would be true when the characters crossed over into film and television), and there were some other radio adaptations of science fiction and fantasy stories that caught the attention as well. Probably the most famous horror-esque fandom of the period is that of The Shadow, and there are still old-time radio fan clubs around today.