I've seen three kinds of parents in this situation. The one's who give in, the one's who get out, and the one's who leave behind the child. Steps I have taken when the parent fails to take some sort of appropriate action include approaching the child and telling them to knock it off, asking them to put the toy back (usually works with amazing ease) and taking my in-store timeout stool placing it in front of the child and asking them if they need a timeout to compose themselves(they stop crying) giving the parent time to exit the store gracefully.
It is extremely aggravating when a parent insists on continuing to shop instead of dealing with their out of control child. Temper tantrum/meltdowns are learned behaviors in many cases, they get some sort of reward for them; be it the toy, cookie, or attention. Even a child, toddler, can understand their behavior is unacceptable. There have been times when I've asked the child to leave the store because their behavior isn't acceptable here. Crying stops, tears stop, and with head down out the door they go with Mom.
Honestly my father had a saying for the faux crying whine, “Stop crying or I'll give you something to really cry about.” We stopped crying then too.
having taken our youngest who is two out a Mex restaurant in Thompsons Station once and to the car where I put him over my knee for a copuple of whacks, he now knows what I mean when I grab him up and sternly ask if he wants to go to the car for a spanking.
My wife....only disciplines when angry or frustrated and is much much more mallebale than me. She will leave a store and give up or on occasion give in.
Many women...especially single or divorced moms do this and it does the kid no favor.
Meterodaddies do it too.
When i lived in Manhattan in the 80s I thought most liberal Jews I knew there were very indulgent with their kids and let them control conversations and whanot...now most GenX and Y parents do that too regardless of cultural backdrop