I am somewhat close to 200 reputation in StackOverflow, which means some ads will be automatically turned off. Some of these ads are relevant to my interests, and I'd rather have the option to toggle.
No, you can't "turn off" a privilege same way you can't turn off your reputation or badges.
Best work around I can think about is using two browser sessions, one where you are logged in, and one where you are logged out. Use the logged out session to browse the posts, and if you see something that requires your account (e.g. voting, editing, etc) switch to the other browser.