It appears to me that the differences System 1 and System 2 reasoning be used as leverage to change one's mind.

For example, I am rather risk-averse and sometimes find myself unwilling to take a relatively minor risk (even if I think that doing that would be in line with my values). If that happens, I point out to myself that I already take comparable risks which my System 1 doesn't perceive as risks because I'm acclimated to these - such as navigating road traffic. That seems to confirm to System 1 the idea of "taking a minor risk for a good reason is no big deal".