Canada

The thing is that this is actually not a vague situation. No one is arguing that parents aren't able to teach their kids right from wrong. The issue is when the parents' values come into conflict with the child's own inherent right to express themselves as one of the protected classes specifically outlined in section 15 of the Charter of Rights and Freedoms. Most topically along sex/gender lines, but also many others.

Thankfully being an asshole is not a protected class so we are free to teach people to not be that.

Children aren't stupid, adults are inconsiderate to how a child functions.

A child is a little person who, just like adults, understands concepts like good, bad, freedom, imprisonment, hungry, tired, etc. the problem is that children are not given a document that speaks their language, the words we use with kids is radically different from daily life. And when a kid uses a grown up word or phrase, we don't compliment them on their defr use of language - we interrogate them with "where did you learn that" or "who told you that". Imagine if we just did something incredible, like publish a phD dissertation and instead of celebration you were grilled with question that might get you in trouble. Or, at best, the adult is happy that the word was used but ignores or doesn't bring it up again? All that work from the kid and they get nothing for it but more work. So why tell an adult at all? Why show off their ability to learn if it gives them nothing?

Adults also use big words for no good reason. They are oblivious to the fact that kids didn't get 12 years of vocab, reinforced through tests and essays. If adults used simpler words, it would not only solve the communication gap between kids and adults, it would encourage a more clear understanding of what words mean to adults. Calling something egregious is fine but saying "for no reason" means the same thing. Adults do not use words that they teach to children, so ultimately kids view adults as using some crazy legalese or second language to talk to each other and make arrangements.

Clean up the language and celebrate kids as people who are always learning, and they will be happy to communicate to you and with you. That's how we, as adults, can use our experience to help protect kids with their own input. It's how kids are taught to be wary of adults - strange danger is out and communication is now key. Talking with grown ups they know to confirm what they are being asked helps make kids who aren't scared of new things. In fact, they will happily embrace the new stuff as long as they know what to expect.

At what point does a child become autonomous enough to make their own decisions about their values?

Middle school-ish. It might make sense to tie it to the age of criminal responsibility (that is, the age at which you're assumed to have enough understanding of right and wrong to be charged with a crime in your own right), which, in Canada, is 12.

Check which community you are posting this to.

Oh of course, I feel like it goes without saying that this is in reference to young school-age children.

My personal opinion, would be that the age cut off for where a child's rights supersede the opinions of their parents would probably be 13 or 14.

Honestly the less rights parents have the better, IMO. They need certain rights just to operate but man, some of them are very shit people.