What was done seems unacceptable, but I always get a little leery of any theatre, especially a community theatre black balling anyone. 

I am sure that the story of what she did will get around, and she has probably eliminated herself from all future productions.  Let that be the end of it, don't make the organization be the bad guy.

Just my $.02, take it for what its worth, especially in this economy.

It's true that they don't call it DRAMA for nothing. And during a run tension/anxiety and nerves are high wich makes a ripe environment for tempers to flare and things to get said, which may not be meant.

I think that this is NOT an "unforgivable sin."  I would certainly think twice on casting this person, and I would make sure everyone else knew about the situation, but in the end, it sounds like this person DID go on stage.  Actors and Actresses have a tendency to do and say things in the heat of the moment that they would never do when cooled down.  It is possible that this person was having a horrible day, got to the theater, had a fight with someone backstage, went out there and had a baby crying during his or her scene, and then came backstage and said that in a fit of frustration.  If you had refused to remove the baby and called the bluff, then you'd have just cause.  

"The Show Must Go On!"
Period.
No exceptions.  (Well, maybe a few, but they're pretty dire exceptions!)

If I have accepted a role in a play (whether under an informal CT arrangement or a formal professional contract), then the only acceptable reasons for me to NOT go on the stage to perform my role are: 
- death (actual or impending, mine or that of someone in my immediate family),
- disease or injury (my own), or
- termination of the contract (by the CT or by me or by both).

Babies, cellular phones, excessive heat ... they're all annoying ... but unless they lead to death, disease/injury, or contract termination ... then my job as an actor is to "soldier on" or "be a real trooper" despite the adversities.  That's one of the "joys" of live theater, is it not?

That being said, a pre-show announcement to the audience or a note in the program about babies, cellular phones, excessive heat, might do a lot to prevent or minimize such annoyances.

I like to hope that the majority of audience members are both smart enough and considerate enough to NOT cause annoyances (I don't bring a baby into the theater during a performance or run-thru; I turn my cellular phone or any other device OFF while in the theater; etc.).

And as for that small and annoying minority of audience members who are either stupid or inconsiderate or both ... well ... again, that's one of the "joys" of live theater.

And if I'm the actor having the prima donna moment, refusing to go on the stage because of the presence of a (?noisy?) baby in the audience? 
Well, if I'm lucky I MIGHT be allowed to pull that kind of an inappropriate stunt ONCE and ONLY ONCE.
- Perhaps there are understandable circumstances that lead to the incident, or not.  I will probably receive a private and firm-but-friendly talking-to by the SM or the Director or the Producer, indicating that this will not happen again.
- If I'm stupid enough to try that inappropriate stunt again, at the very least I should not be cast in a show by that CT for a VERY long time, if ever. 
- If I am a paid professional actor, and I try to pull that inappropriate stunt a second time, I would probably be fired on the spot and replaced by an understudy of some kind.

I am, of course, reminded of the recently released recording of Christian "The Dark Knight" Bale, having a verbal meltdown on the set of some recent movie of his.  The acting product he provides has to be worth AN AWFUL LOT to put up with that kind of inappropriate behaviour.  Many Hollywood actors who have demonstrated an ability to be "difficult" have had trouble getting roles, unless their acting product is SO spectacular that their "difficult" personalities are overlooked for reasons of Box Office.  I doubt that most CT's have that kind of leeway.