JERUSALEM — For as long as she has anchored her own television news program — about five years, in different iterations — Lucy Aharish has always opened by greeting her viewers in both Hebrew and Arabic.

It’s only natural: She is Israeli — born and raised in Dimona — and Arab and Muslim, the daughter of parents who moved to the south from Nazareth. Her frequent monologues are a trademark and have sometimes resonated far afield: Impassioned diatribes about the failure of both the West and Arab leaders to protect innocent victims of the Syrian civil war were seen by millions of viewers worldwide.

Yet, because so few Arabs and Muslims have prominent roles in Hebrew-language news in Israel, and because racism is so commonplace in Israeli society, Ms. Aharish says, she continues to receive a steady supply of hate mail merely for adding “masa’a al-kheir” to the “erev tov” she wishes her audience at the top of each weeknight show.

She ignores most complaints, but one letter a month ago stirred her interest. The anonymous writer called her Arabic salutations “inappropriate and very jarring,” and said it was “improper” for the station to allow them. Yet the writer sounded respectful, and closed with an old-fashioned Hebrew expression: “Alu v’hatzlichu,” or “Go forth and succeed.”