We don’t go to synagogue to pray to a flag,” Mr. Naman, 63, recalled having said in a recent telephone interview.

That rabbi acceded to the request. So, after being transferred to North Carolina and joining a temple there six or seven years later, Mr. Naman asked its rabbi to remove the Israeli flag. This time, the reaction was more predictable.

“The rabbi said that would be terrible,” recounted Mr. Naman, a retired paper company executive who now lives outside Jacksonville, Fla., “and that he’d be embarrassed to be rabbi of such a congregation.”