Priests are, as this myth rightly says, prohibited from the shedding of blood. However, there are quite a few Church canons specifically prohibiting clerical participation in warfare.

This is not to say it didn't happen - La Chanson de Roland has Bishop Turpin in full armor, and the frequent repetition of canonical decrees is usually inferred to mean the existing rules are probably being disobeyed - but in that case there would be no particular need to restrict oneself to a mace.

So yeah, just another medievalism.

The Knights Templar were originally a monastic order, though not priests per se, and I can't find any evidence that the chaplains actually fought.

There is, however, evidence of 'war clerics' like those you're probably thinking of. The Bayeux Tapestry depicts a Norman Priest wielding a mace - Bishop Odo of Bayeux. It's a theme that stretches through much of Scandinavia and those of Scandinavian descent. Bishop Absalon of Roskilde led a military campaign against the Wends of Eastern Germany.