Two things.

1)    There is no hard and fast distinction between old-time and bluegrass.    The string band rendition of "Little Black Train" could be considered bluegrass. Red Clay Ramblers could be considered either.   There is no point to arguing about terminology on this. Carter Family of course predated the term bluegrass but much of their material has been done excellently by bluegrass bands--with exactly the approach taken in the string band version.

2) Consider an atheist version of "Little Black Train".   A non-starter.   The words--and the message (whether you agree with it or not)-- are one of the elements which make this a strong song.