It's my birthday so no one is allowed to bust my chops.
I ump, I coach and I play. As an ump I am certain that I have never taken my irritation with a fan/parent/player/coach out during the course of the game for which I am a paid professional. I am also certain that there are numerous aforementioned folks that believe that I have done exactly that. Over the years of coaching and playing I am just as certain that other umpires have done it to me or my team - different perspective.
When faced with a parent/spectator as described: ignore, ignore, ignore. If it is really out of line, give them a choice to continue watching the game from the present location without the critique; move to a remote location or leave the facility and find out from their son/daughter/friends how the game turned out.
Maybe I have been lucky over the years, maybe it is my sparkling personality, maybe I just block them from my memory - I can only recall two times over 25 years where anything got beyond just a conversation between me and the agitator.
It is one of the few professions where you can be successful 99.9999999% of the time and still be the biggest horses b--- in the world.