I'll preface my remarks by saying that I do a lot more ASA games than I do NFHS games.
That said, I think it would be easier to address on the HS level because of the game managers that are typically on site. My first conversation would be with the coach of the offending team.
The rules don't allow for players or coaches to be behind the backstop. If a parent/fan is being obnoxious, I'd ask the coach to address the behavior.
I understand that there's likely to be a split of opinion about what umpires should or should not do in these instances.
A well coached team could find ways around this. Of course all of this assumes that a pitcher can actually hit the target that the catcher is calling for. I know you've all done games where the pitcher isn't in the same zip code. In any case, a few faux outside targets that result in a bit of chin music will quickly put the parent's calls of pitch location in question. Again, assuming the pitcher actually has that kind of control.
I'll say I've had more issues w/ ASA games than HS games. I've only tried addressing issues on the other side of the fence a few times. One time my partner and I were discussing potential strategies between innings. The catcher must have overheard part of the conversation because on the next close pitch, our heckler started in again only to have the catcher turn toward the fence and yell out "Dad! Shut UP!" Now there's a catcher that knows how to call a game!