As a data-point, I’m a rationalist, and a subscriber to the New Humanist, which is published by the Rationalist Association you mention, and is the descendant of the 1971 magazine you mention titled ‘The Humanist’.
So I fall into the intersection of LW rationalists and “1950′s rationalists”.
Wikipedia:
The New Humanist has been in print for 131 years; starting out life as Watts’s Literary Guide, founded by C. A. Watts in November 1885.[4] It later became The Literary Guide and Rationalist Review (1894–1954), Humanist (1956–1971) and the New Humanist in 1972.
As a data-point, I’m a rationalist, and a subscriber to the New Humanist, which is published by the Rationalist Association you mention, and is the descendant of the 1971 magazine you mention titled ‘The Humanist’.
So I fall into the intersection of LW rationalists and “1950′s rationalists”.
Wikipedia: