A “public anathema” would be an excommunication. In so far as Muslims weren’t part of the Christian or Catholic communion, there would be no excommunication or anathema of Muslims, though a Christian who espoused such views could be excommunicated or anathematized.
Yeshua (”Jesus”, if you will) was pretty much “Anathematized” by the Jewish Sanhedrin or dominant religious institution of his time, wasn’t he?
Is it a sin to be anathema to an apostate religious institution (”Church”)?
...Or is it a sacred obligation?