After nonprofit giant Ascension Health closed the doors on Detroit's Riverview Hospital, the only hospital on the city's blighted east side, some residents directed their anger at St. John Hospital and Medical Center, the system's lone remaining outpost in the Motor City.

In renovations at St. John, the local Ascension subsidiary moved the lobby so that it overlooked the wealthy and almost exclusively white suburb of Gross Pointe Woods rather than Detroit, which it had faced for more than 50 years. William Anderson, who had...