I think the backlash to describing Heinlein as "fascist" says more about the average person's understanding of real-life fascism than anything. I get the impression most people just replace the word with "evil" in their head rather than considering it on its merits and understanding what his thoughts on it were. There's often an implicit unstated argument there, like "X author is fascist, fascism is evil, therefore X author is evil, therefore you should not read their books", which seems a little more extreme than is warranted.
On that note, Heinlein wrote all sorts of weird, contrarian themes into his books. Many of them pushed against the prevailing social norms and beliefs of the time, from sexual norms to ethics to race relations. Trying to pin down his actual beliefs is difficult because he would often write one book taking one stance on an issue, and another later with a totally contrary stance. Often when I read Heinlein I find myself strongly disagreeing with what he's putting down, but fascinated with the question or angle being posed/presented.