Option to make cape private on profile

I have a MineCon cape on my account. When I wear it, people message me across multiple platforms on the internet and my private email obtained from data leaks. They inquire to buy my Minecraft account since it has the rare cape.

I've read online that others also get phone calls and text messages if their phone number was tied to their email. I'd also wager that MineCon capes are targets for phishing and hacking attempts, based on some of the high offers I've recieved.

There are sites online that lists every username that is wearing a MineCon cape. I'm guessing this data is coming from an API or something on the Minecraft site.

I no longer equip this MineCon cape because I don't want to deal with these messages anymore. An option to make your cape or your profile in general private would be helpful.