Monsterpal wrote:
Heinlein was as famous as Bradbury then and now, as far as his contemporaries go. Heinlein was published in the slicks earlier and wrote many more novels than Bradbury, but they're both still very well known by the general public, as are Asimov and Clarke. But we're talking about work from fifty to seventy years old here, so much of it's bound to be dated.

All I get from this discussion is the impression of two men with differing memories of an event far in the past. I'm not sure Alland's politics is really at issue here, but I'd be surprised if the extremely conservative Bradbury held that against him.
Bradbury was a flaming liberal in the 40s and 50s (just as Heinlein was in the 30s); his politics have drifted rightward since then.  But no, Heinlein most definitely was not as famous as Bradbury in the late 1940s and early 1950s, though he was published in "regular" magazines (including Boys' Life, a well-known magazine for guess what).  I think this kind of stuck in Heinlein's craw.