Look for a bank or credit union that is a "portfolio lender". That means that they write loans backed by deposits. Portfolio lenders usually have better terms and tighter underwriting standards. There aren't many of these left.
If you define "stupid" or "immoral" to include an adjustable rate mortgage, you will not be successful. Some religious or other special interest groups have specific banking requirements... there is a Lutheran financial services company, banks that observe Islamic financial principles, Unionized banks, credit unions for specific churches, etc.
ARMs make alot of sense for many people in various situations. For example, if you were in the military with a 5 year assignment somewhere, why would you pay a premium for a 30 year loan that you will never need?