There is at least some evidence suggesting certain methods work better than others, most of the time.

Yes, but the average professor of medicine who preaches evidence-based medicine doesn't study those methods.

He also doesn't run controlled test together with other medicine professors to find out how to teach medicine most effectively. He still doesn't feel like a hypocrite.

No one who is paying attention believes their money is safe anywhere, let alone the stock market.

If you ask them specifically they might deny to hold that belief, but they usually don't walk their talk in the sense that they apply the student they preach with their philosopher hat to the decisions they make for their retirement money.

Some Christians are compartmentalizing on a much more significant level.

Not really. If you retirement funds get wiped out that a significant life event. If you believe in God and he doesn't exist not much bad happens.

Beliefs with a high cost of being wrong are significant.