Statistics and reasoning are almost always applicable, and that's the extent science is applied to most fields.
If you want people to act in an evidence-based way without invoking trust/faith, they need to understand statistics and be able to evaluate studies on their statistical merit. Unfortunately that's quite difficult and the educational systems we have do a poor job of teaching it.
Statistics is subtle. For example, "It turns out, most doctors don’t know actually know probability." https://blogs.cornell.edu/info2040/2014/11/12/doctors-dont-k...