Most people who hate FDR hated his policies, the people who hate LBJ hated him personally. Big difference (plus many were people on his side, not opponents).

As for the rumor, I am going on a very old memory, and I'll be the first to admit that it sounded like "Texas reactionary redneck rumor mill kind of thing" at the time, but in trying to find something about it (didn't, the original election seems more of corruption than murder), I did find out a couple of books listing his relationships with a couple of men who did engage in murder (including one that murdered his sister's boyfriend and that LBJ later hired). So there was a swirl of rumors around the guy, which again sort of shows what most people thought of him (even if the rumors are not true).