It's easy enough to accept if you think that the questions Heinlein felt strongly about were mostly not part of the conservative/liberal distinctions of the time. For example, there were plenty of people all over the political spectrum who thought that women shouldn't have paid work (at least not in peacetime, not if the work wasn't doing other families' housework, not unless it was volunteer work when no men were handy, etc.), and would have agreed on the value of a strong military. (Just picking two that Heinlein seems to have agreed with, at least some of the time.)

That's separate from both the idea of being persuaded by someone he's close to (you love someone, you're more likely to take their arguments seriously) and the idea that there are things he might not care enough about to maintain a position on, if not doing so caused stress at home. (A male version of the character in Job saying "I certainly don't disagree" when someone asks her opinion of her husband's fringe beliefs; when alone she explains to him that she doesn't think husband and wife should argue in public, with the implication that if either of them takes a strong position in public first the other should back it.)