Police departments in at least five states are investigating, and in some cases condemning, their officers' social media feeds after the weekend publication of a database that appears to catalog thousands of bigoted or violent posts by active-duty and former cops.

The posts were uncovered by a team of researchers who spent two years looking at the personal Facebook accounts of police officers from Arizona to Florida. They found officers bashing immigrants and Muslims, promoting racist stereotypes, identifying with right-wing militia groups and, especially, glorifying police brutality. All the...