I guess the first thing to understand is whether you are Enrolling these devices and whether these settings are set to Automatic Push or Manual Download. If anything is set to Automatic Push, it gets pushed at the time of the enrolment, based on the User (that logged into My Devices) and the Device they logged with (and any subsequent User Groups or Device Groups). These Settings do NOT appear under the Profiles tab in My Devices, and when you're looking at Profiles in System Administrator, they are not listed as separate Profiles, but rather as settings under the Device Management Profile.
With Manual Download, the Profiles show up in My Devices -> Profiles for the user to selectively apply. Unfortunately, this does not seem to work with Device Groups or Devices. While it does let you set them to Manual Download, I was not able to get them to show up in My Devices -> Profiles. Only User & Group Profiles set to Manual Download showed up for me there. So, you would need to use a different distribution method for Manual Device and Device Group Profiles.
Gerben Wierda wrote:
So, if I let a specific user install a Parental Controls profile that is available for a device that is enrolled, that Parental Controls only applies to that use and not to any other user? Because, how do I get that profile to the user if he goes to mydevices?
And wouldn't the user be able to just remove that profile?
So, that kind of profile download would not be possible. It would have to be a User or Group Profile or you would need a different distribution mechanism. But if you were to generate a Device or Device Group profile and download it from Profile Manager (not My Devices) and transfer and install it, since it's Device or Device Group, it would affect all users.
But if you made the profile a User or Group profile, it would be available for user download at the My Devices Portal.
Regarding removal, you can set rules in the General Settings. Options are Always (removable), With authoization, or Never:

So you could either install these on the users' behalf, or perhaps include a necessary carrot in the Profile like proxy or network settings.