That would go against the happy ending the writers wanted to create. Monroe and Rosalee disapproving of their kids participating in these missions would contradict the "fairytale" overtones of the final ten minutes. They certainly couldn't be that "one big happy family" if that were the case.
I really don't think Monroe and Rosalee thought like Vito Corleone when he didn't want Michael to be involved in the family business. Like it or not, Nick's business became their business. That's why they did things like immediately checking in with Nick as soon as they returned from their honeymoon. Rosalee was still taking an active part in missions while she was pregnant as seen in Tree People. Monroe and Rosalee both see what they do as part of becoming better people so I don't think they'd be terrified at what their children are doing. They simply don't see Nick and what he does as something so horrible. Monroe has even encouraged Nick to be more of a traditional Grimm when he felt it was necessary.
I really don't think Monroe and Rosalee thought like Vito Corleone when he didn't want Michael to be involved in the family business. Like it or not, Nick's business became their business. That's why they did things like immediately checking in with Nick as soon as they returned from their honeymoon. Rosalee was still taking an active part in missions while she was pregnant as seen in Tree People. Monroe and Rosalee both see what they do as part of becoming better people so I don't think they'd be terrified at what their children are doing. They simply don't see Nick and what he does as something so horrible. Monroe has even encouraged Nick to be more of a traditional Grimm when he felt it was necessary.