The song in question is “Like a Sunday in Salem” by one Gene Cotton. I don’t recall the song when it was popular and can’t find any info on the singer to determine if the lyrics are America-esque nonsense, Dylan-esque not to be taken literal imagery, or what. I assume the Salem part refers to Salem, Mass but have no idea how that would relate to Amos & Andy. Anyone know?
Lyrics here.
My guess is that this song is about the anti-commie “witch hunts” led by Senator Joseph McCarthy.
There were some people out in Hollywood
The words they had spoken it was well understood
But three thousand miles and for ev’ryone’s good
A man stood singing his song
The first two lines could reference the screenwriters that were blackballed because they refused to “name names”.
Sounds good, but where do Amos & Andy fit in- were they called to tesitfy? 
I think that’s just to help with the time frame. The radio program lasted until 1960.
Notice this item from Ebay:
http://cgi.ebay.com/Gene-Cotton-MINT-45-rpm-7-PS-on-ariola-SUNDAY-SALEM_W0QQitemZ140146564867QQihZ004QQcategoryZ306QQrdZ1QQssPageNameZWD1VQQcmdZViewItem
However, the Lights Out television show was only on the air from 1949 to 1952. Incidentally, one of its writers was Ira Levin, who died earlier this week.
The Hollywood Ten had been cited for contempt of Congress in 1947, but Joe McCarthy carried on with his “witch hunting” until being condemned by the Senate in 1954.
And the last two could well refer to Woody Guthrie, who was blacklisted during this period.