Can parents refuse to give a child citizenship?

No, but they can just never apply for any proof of citizenship and as long as the kid stays in Canada no one will the US will even notice. Occasionally the IRS mails letters to US/Canadians living in Canada reminding them to file their US tax returns. Those people generally just ignore this and go on with their lives.

No.

And the "paying US taxes" part only becomes reality if the child makes silly money. If he or she only makes $100,000 a year and pays income taxes to Canada, they owe Uncle Sam not a dime. But if that child makes millions a year, they should hire a tax attorney who converts income into investments.

Lets say this accidental American makes $1 million a year in income. Few people spend a million on living expenses. So if that person spends $200,000 a year, the remaining $800,000 would be invested. And after paying income taxes on the $200,000 in Canada, very little money would be left for taxation in the United States.

However, a person who makes a million a year is most likely smart. And a smart person with US citizenship would definitely leave cold Canada behind and do what Elon Musk did: move to the best country on Earth.

Since it is automatic citizenship based on jus solis - birth in the jurisdiction - the parents have no control over it. They should have avoided travel while pg. They are responsible for filing their child's income tax returns, if the child has any income (e.g. investment income from investments made on the child's behalf), until the child turns 18 & becomes a legal adult responsible for their own tax returns. At that point, the child can renounce, if they wish, but until they renounce & receive their Certificate of Renunciation, they must file & pay US taxes as required.

Can the parents refuse citizenship on behalf of the child. NO

Where do you expect the child's Birth Certificate to come from? The province of... or the state of ...

The child is born a citizen of two countries. The way it is.CHILDREN have rights too.

The CHILD can when an Adult give one of them up if they want too.

Millions seem to live quite easily with this burden on both sides of the border.

Should the parent for some reason be able to cancel one of them the child when 18 can get it back if they want it.

Hint they present their birth certificate from the state of California.

Paying taxes is not always the case. The IRS just wants the paperwork. Canada and the US have a tax treaty for situations like this. Credits are given for taxes paid in the other place where the income came from.

YOU DO NOT PAY DOUBLE TAXES.

There are two kinds of 'accidental Americans'; those who happen to have a US citizen parent but who were born and brought up in another country and those who were born in the US to parents who are from another country.

For the first group, it is very simple.  Parent can just not file a consular report of a US citizen birth overseas.  Nobody will be any the wiser.

For the second group it is a little harder because the US has a peculiar rule; mandatory citizenship for anyone born on US soil.  That means that the moment anyone opens your non US passport, they will assume that you are a US citizen.  Yes, it is a problem but not one that is hard to solve because you can renounce your US citizenship without penalty at the age of 18 in front of a consular official.  You may have to show that document if you want to open a bank account in a European country (FATCA) or visit the US.

That child is ELIGIBLE for citizenship.  That doesn't make them a citizen automatically.