Can an employer monitor employees off-premises or during activities not in course of their employment? Can they fix what people can do in their day to day life and activities in any way? For example, an employer dictating what brand of products may be used in the employees' day to day non-working life.
An employer can require their employees to obey lawful and reasonable directions. In this conduct a reasonable direction is one which would prevent a significant adverse effect to the employer and is a reasonable imposition on the employee given their role in the organisation.
Even without a specific instruction, an employee owes a duty to their employer to not damage their reputation.
McDonald’s can require their staff not to frequent KFC while in uniform.
Celebrities who are brand ambassadors can be prohibited from using conflicting brands.
A church leader could be prohibited from extra-marital affairs.
General limits on social media so as not to reflect the employer in a poor light.
I know that some German banks didn’t allow employees to have loans or mortgages with other banks, presumably for security reasons - you don’t want other banks to be able to put pressure on your employee who has problems repaying a mortgage. On the other hand, these banks had much more generous terms for employees, so this wasn’t a problem; employees actually saved money this way.
There was an interesting case in the UK: If you claim you are ill, so you can’t work and the employer still has to pay you, the employer has the right to check that you are telling the truth. What made it interesting was that the case was about a police officer who claimed to be injured. And while the police wouldn’t be allowed to check on a random citizen, they are allowed to do this if they are the employer.