According to the privacy policy:
Other than on Careers, we won’t share your personal information with non-agent third parties unless we are required to do so by law, or if we believe in good faith that disclosure is reasonably necessary to protect our property, rights or those of third parties or the public at large.
The "Legally Useless Summary for Short Attention Spans" version:
Outside of when you apply for job listings, we don’t share your personal info with anyone.
It's possible to add a Google+ or YouTube profile to your Stack Exchange profile page. But we don't do that for you. It's also possible to put things, such as a distinctive avatar or display name, in your profile that will allow others to identify your Google+ account. Again, that's your choice, not ours.
Now, if you use Google as your OpenID provider, there is a connection between that account and your Stack Exchange account. But neither Google nor Stack Exchange expose that connection to third parties. I had to add my Stack Exchange profile to my Google+ about page manually; it wasn't added automatically. Google has its own privacy policy that you might want to examine.
If you are still concerned, you can use any number of other OpenID accounts, including the Stack Exchange OpenID system, to register your account. It's easy to change and we don't mind.