Personally while attempting to contradict a higher-status belief I readjust my goals. Rather than completely convince my audience I try to create some doubt that the higher-status belief might be wrong. I have found that effective ways to do this is by using sentences like "I am not sure either, but what about..." or "Hmm, but what would then happen if..?", this way not only does the audience think that they are the ones coming up with the conflicting ideas (instantly boosting their confidence in it) but also it doesn't look like you are actively challenging anything's status but rather are a confused ally, putting the audience on "your side".
Of course the drawbacks are that this can be done only so often or people will start to think you don't know anything at all and sometimes your audience cannot come up with your answers to the questions ('derailing' the conversation). But as a general rule I try not to tear down high-status ideas from a low-status position - why pick a hard fight when you can also split it into two easy fights.
I was reading reviews of HPMOR on Goodreads and I noticed that the people who didn't like the book were essentially "put off by the rationality". They thought Harry was arrogant and condescending.
Then I was thinking, a lot of people are "put off by rationality" for similar reasons. What a shame. There's a lot of value in spreading rationality, and this seems to be a big obstacle in doing so.
Any thoughts on how to make people less "put off by rationality"? I think the core issues are: