Trouble is, sometimes people feel uncomfortable bringing up the subject, so it takes the professional who is calling bringing it up to see any benefit.

I do not think that a checkbox is appropriate - at any point, you might become concerned with the privacy of a matter, or you might not realize that privacy is a concern for you. For instance, consider someone who accidentally listens to a message stating that they are now pregnant, at work. Their employer now has advanced notice of a pregnancy, but no knowledge of the employee's intentions with regard to work. That is going to change the dynamic of the workplace, even if the employer does not intend anything nefarious. I really think the only graceful solution to this is agreed code words.