Quoting the article:
This is a guide for how to truly opt out of this feature...
To be clear, everyone who does not have a parentally controlled account has in fact opted into Real ID, due to a security flaw. Addons have access to the name on your account right now. So you need to be very careful about what addons you download -- make sure they are reputable. In order to actually opt out, you need to set up parental controls on your account. This is not an easy task. Previous to the Battle.net merge, you could just go to a page and set them up. Done. Now, you must set up an account as one that is under parental control. Once your account is that of a child's (a several-step process), your settings default to Real ID-disabled. Any Real ID friends you have will no longer be friends. In order to enable it, you need to check the Enable Real ID box.
Setting up parental controls:
Go to the appropriate battle.net site for your region. (That link should take you there.)
Push the Create or Manage a Battle.net Account button.
Log in as normal.
Click on Parental Controls, which is an option listed under Manage My Games. (And, if you're like me, you'll be sad that you are still not in the beta.)
Choose the No - Setup Parental Controls button.
Fill in your info as both the child's account and your own. (Why they make this distinction, I don't know. Parental controls always used to be an option for adults to manage their own game time.)
You will receive an email. You need to save this email, because the link in there is the only way to get to the parental controls. Otherwise, you have to make Blizzard resend it. Click the link to get into the controls.
Save Settings and then be told it will take up to 30 minutes to go into effect.
That is how to opt out.
It says that it's not easy to set up parental controls, but it only took me about 5 minutes total to do all of that, so really not that bad. It looks like it works well - logged in to test it and I didn't see any of the RealID setup settings in the Interface menu or the Social tab. Seems to have done the trick!
I think it would be much better if this was standard across all accounts (not just in parental controls); what would be best is an Opt-in setup where you're automatically out of RealID until you select that you want to activate it. That would be the safest for privacy, really. At least Blizz listened to the community and decided to cancel their plans for using RealID on the forums.