It's true that the scientific method is not necessarily the best tool to handle other people. As I've discussed previously, science tends to say "never attribute to malice what can be adequately explained by incompetence", even where a wise man would be saying "once is happenstance, twice is coincidence, three times is enemy action". Science tends to downplay the importance of individual correlations, secure in the knowledge that in the long run any genuine effect will show up again.
Most skeptics are aware of this. The scientific method to us is an ideal: if you have the time to apply it fully then that's wonderful, but in most cases that isn't an option. So to say "skeptics disagree with irrationality" is simplistic. In reality, our position is more nuanced. One statement of it would be:
It’s OK to be irrational as long as you don’t treat your shot-in-the-dark guesses as the final word, and are willing to discard them when better options come along.
That has applications far beyond the study of nature.