Our company calendars are shared across the company, when you are going for a dr's appointment can your employer insist on having those event made "public" to all staff.
For example: A manager is going for a personal dr appointment and it is of sensitive matter and but the calendar must be visible so other members of the team can see when the manager is available to schedule meetings. If the Dr appointment is private in the calendar does the employer have the right to request that it be made visible to the whole company?
You do have a Constitutional right to privacy. The lines between labour issues and Constitutional rights issues are sometimes blurred, and this is such a case.
However, it is possibly the best course for you to keep such medical appointments as general or vague as possible in terms of their description on the company calendar - perhaps by simply calling them "Medical Appointments." This will help you to avoid any conflict and still preserve your privacy to a large extent.