Can I change the public / private setting for my published ideas?
It is not possible to make published public ideas private or vice versa.
If users were able to make specific public ideas private, there would be a way to hide (formerly public) losing trades from the community. And if users were able to make specific private ideas public, there would be a way to showcase winning (formerly private) trades, while keeping losing ideas private. As a consequence, the ideas tab on the profile page of a user would not necessarily present a complete picture, which would violate the principle of transparency that TradingView upholds.
Please note it is of course possible to republish a private idea as a public idea.