Agreed, unless Charlotte gives the ok for a date, which is quite likely what is going to happen seeing the screenshots shared not long ago.
At the end of the Day, the MC should express his concern if Emma goes to a date alone with Zak, but if the employer (Charlotte) says it's ok, that's it. I believe we had that happen to a lesser extent already, where Charlotte told the MC to do an action he was against.
Assuming it goes along those lines, or that the MC keeps an eye out, if Emma gives the ok, he'd have no grounds to stop it from happening if it looked like a normal teenage date, which if Zak is not entirely stupid, would be what happens. I mean even to a bodyguard, Emma giving herself to the man she adores, is hardly a suspicious action regarding his job.
At this point, while some bounds are formed, he's not yet the father figure, or involved with the mother either.
As such, while he can object on security grounds to some things, he's got nothing to say regarding how they deal with their private life or with their lovers outside of the security concerns he should mention.
All things considered for a bodyguard, he's probably overstepped his job more than once already, but, being a VN, we'll ignore those