The problem is that this outlook is often used as an argument in favor of some heretical position, instead of just being a defense against outright rejection. What is often forgotten (aside from the excellent points brought up by mcv) is that Galileo and Darwin were each among the very top experts in their respective fields, and many of those who rejected them most forcefully were laymen. That was the biggest difference between them and their detractors -- they were experts facing off many laymen and amateurs -- not their heresy. These days laymen often challenge experts and see themselves as Galileo just because their opinion is heretical, rather than because they've studied a subject more rigorously than others. Rigor and scholarship must precede heresy.

Another pitfall that's common nowadays is that many ideas that are presented as heroic heresy are just yesterday's rejected dogma. When dogma is rejected when a more rigorous heresy shows up, it doesn't lend more credibility to the rejected dogma, which is now heretical. In other words, these are people who claim Galileo's heretical status by arguing for geocentrism, which is today's heresy. Ironically, these days it is mostly reactionaries rehashing old dogmas that proudly describe themselves as heretics.