But I do think that a good parent would grant their kids a certain level of privacy and autonomy, depending on the child's age and the risks involved.
In this case, the risks of a kid eating meat are fairly low; one kid's chicken tenders aren't going to build a factory farm, and they can always change back to a vegetarian diet later.
(Of course, some vegetarians will have stomach issues if they suddenly start eating meat. The kid should know about that risk, but the reactions in question are usually very mild.)
Funny story though - we have a family relative with younger children who was raising them strictly vegetarian. No meat (the mother insisted), though the dad quietly admitted he eats meat on occasion much to her chagrin. On a family vacation the children were left at the house for dinner, and another relative began preparing a chicken dinner.
The conversation between that relative and the children went something like this:
"Dinner's ready! Come get the chicken!"
"This doesn't have meat in it, right?"
"What? Well, it's chicken!"
"Right, but does that have meat in it?"
"Well... No... Certainly not. This is bona-fide, 100% pure, Grade A Chicken. Now eat!"
Somewhat irrelevant, but: do parents actually have a right to enforce a no-meat diet on their kids?
I understand (say) having a "no meat in the house" rule, telling your kids not to buy meat products with your money, and/or only cooking vegetarian food.
But requiring your kid to adopt a vegetarian diet at all times seems to me like an extremely controlling thing to do.
Maybe it's OK at age 5, but once the kid is old enough to understand the distinction it should be entirely their choice.