Official NFHS Rule
Rule 1 Section 5 Player Equipment
Article 3 The catcher shall wear, in addition to a head protector, a mask with a throat protector, body protector, protective cup (male only), and baseball protective shin guards
Article 4 The catcher's helmet and mask combination shall meet the NOCSAE standard. Any helmet or helmet and mask comination shall have full ear protection (dual ear flaps). A throat protector, which is either a part of or attached to the catcher's mask, is mandatory. A throat protector shall adeuately cover the throat. The commercially manufactured catcher's head, face, and throat protection may be one-piece or multi-piece desgin. While in a crouch position, any non-adult warming up a pitcher at any location shall wear a head protector, a mask with a throat protector and a protective cup (male only).
So the rule would be as long as the ears are covered it is ok.
Major League rules which the MIAA play by:
Rule 1.16 D All catchers shall wear a catcher's protective helmet, while fielding their position.
So I am not sure where the whole must be hockey style mask is coming from with the umpires.