I guess, though I don't like your examples.

Professors who teach evidence-based medicine at universities generally don't have any problem with the fact that they use non-evidence-based teaching methods to do it.

I don't know of any 100% certain way to impart knowledge. There are techniques that teachers use that help the transmission of knowledge. There is at least some evidence suggesting certain methods work better than others, most of the time.

Very skeptical philosophers still think that they retirement money they invested in the stock market is safe.

"Safe" is the key word. No one who is paying attention believes their money is safe anywhere, let alone the stock market. There is a risk, and people, professor or otherwise, guage the risk and reward when they decide whether to invest.

Some Christians are compartmentalizing on a much more significant level. On one hand, they go to the mechanic if their car needs repairing and the accountant if they need halep with their taxes. On the other hand, they believe in invisible winged creatures and invisible horned creatures who are doing battle over the eternal destiny of souls in a very real ethereal spiritual plane of existence.