Is it standard or even typical as a form of disciplinary action for an NCO to call a soldier's parents to complain about the service member?

Not typical, but I have seen it (usually younger Soldiers). The goal is not to embatass you, but to change your direction. Family can have a positive influence. If your NCO truly thought you were a dirt bag they wouldn't have bothered to call. I assure you it wasn't done lightly.

I had a sergeant try to tell me to call my wife when I had an incident of missing pt and was late for school during my stay in Pensacola for A-school. I told him no and I will not give him that info. Told him if he was going to do it that he needed to find that info on his own. He sent me back to class and that’s when my instructor who was a First Class Petty Officer, rip him a new hole for trying to do that. Sergeant was my class advisor. PO1 threatened she was going to write him up and had no authority to call my wife who was pregnant at home at the time. Sergeant came back later apologizing for the situation. A-School 2001

This is funny to me, because usually the parents or wife / girlfriend called me. You see I always built a relationship with the family, cause
If anything happens to them they knew me, and if there was punishment it was called for, as one mother told her son,
“ I know Sergeant Blair”
You had to do something very wrong for him to do this. That being said if that relationship was not in place before, it might seem out of place, to make that call now. That is a grey area.
NCO’s responsibility is to
1. Train
2.mentor
3. Discipline
Soldiers, and if your soldiers don’t trust to to come to you with their deepest concerns, then you as a NCO needs to ask yourself why not.

Lastly in the NCO creed doesn’t it say something about punishment and reward???
AATW!!!

It is unusual, but not unprecedented. My niece, when in the USAF, was a "problem child," and her unit called her father. A bit different ... she was getting an admin (honorable) discharge and her Colonel called her Dad to tell him she planned to stay in California, and suggested that she'd get into (more) trouble. Dad drove out and brought her home - that was 20 years ago and it ended happy.
I had a PV2 who was, frankly, an idiot. I wanted to call his parents; but his fathter-in-law was a retired Major and his wife (obviously) was an Army brat - literally a brat. She repeatedly had the PV2 file IG complaints until finally, the IG recommended admin action. BOOM - discharged.
Consider yourserlf lucky that the SFC cared enough to seek parental input and perhaps parental counselling. NCO's never know what kind of parents soldiers have, so it's kind of a crap shoot as to wether or not a phone call will do good or bad. Since you are concerned, it "seems" like your parents care and the call was probably a good thing - if nothing else, embarrassing enough to make you think twice before you lip off to any authority in the future.
I hope the only action was a butt chewing; maybe a counselling statement and no Art 15. Take it as a learning experience ... we've ALL "been there, done that."

I have never called a Sailor's parents and would only do so to either pass on good information or if the Sailor was in the hospital and the sailor was ok with it (or was not responsive). To tell parents their son is a dirtbag, is reprehensible and a clear indicator that the "leader" was no leader.

Nope, its completely unprofessional to contact the family of another servicemember unless they have been involved in a life threatening situation or have died. If the individual has a close enough relationship with the servicemember that it would make sense for them to contact the family from a personal standpoint, thats a bit of a different story, but from a professional standpoint, the servicemember was old enough to sign his life over to the military and should therefore be the only one responsible for failing to uphold the standard. Requesting next of kin info is only for official notification purposes.

I can't imagine that SFC has any respect from her Soldiers once they found out. What does that say to her 1SG or commander about her ability to lead?

This is way out of bounds for an NCO to contact a soldier’s parents for non life threatening reasons. There is absolutely no reason for this to occur. She should be reported to her commanding officer for this.

The goal as your leader is to bring out the very best in you. Sometimes that involves unorthodox means, like calling your parents. The military isn’t just any old employer. That’s why your command resorted to things that would never happen at McDonald’s. You signed on to a whole ass lifestyle when you enlisted. Your commands job is to do everything within their means to make you be the very best you are capable of. In every aspect of your life. Not just a good soldier. We’ve been turning children into adults and adults into fighters for over 200 years, and we’re pretty good at it. Get with the program.

Now I personally do not know why a SFC would call in a lower enlisted person who had gotten in trouble while in the military whether the event happened on base or off base, but the military (in which I served in back in 1979 through 1992 did NOT obtain a phone number from the enlisted person whom had broken specific military regulations whether on or off the base, just so that I could contact this enlisted person's parents to notify them that their son or daughter was a complete dirt bag or waste of a human being who doesn't desire the privilege of breathing air from the same room as me, I mean exactly what in the hell has Uncle Sam's misfits turned into anyway!!!??? Seriously?? Please tell me this is a joke!! Why in the world would an NCO, or hell, an officer or even the C.O. obtain the parents phone number from som dirt bag member of the military, to what?? Call their mommy and daddy to tell on their kid?? Maybe to have the parents place the service man or woman in a time out or some BS!! Uh... I mean WTF!! This question that I am responding to... Is the OP, serious?? Please tell me this is some kind of joke!! I mean I had heard that there has been significant changes in the military since back in the days when I served!! But, come on people!! Exactly what has become of the military if this is the case?? So what? Does everyone just hold hands and sing Kumbaya together around a fire, roast marshmallows and instead of carrying real weapons to defend this great nation, instead are issued their equipment from someplace like TOYS-R-US or some similar store??