iMessage disabling the face team

Do you mean Facetime gets deactivated if you try to log onto iMessage?

If you use a real Macs values you also need to use it´s MLB an ROM value to get iMessage and Facetime working. Facetime seems to be less strikt as iMessage so Facetime normally works even if the passed values are not 100% plausible while iMessage doesn't. Since both share some Certificates any attempt to sign into iMessage with not 100% plausible config will result in deactivated Facetime as well. Be careful! Do not play to much with these values since every change will associate a "new" Device with your AppleID the more devices assigned to an appleID this way the more likely Apple will blacklist your AppleID for iMessage and Facetime on non 100% genuine Apple Devices.

Most likely that´s what happened. Apple keeps an eye on an AppleID´s activities and if your actions look suspicious to them they simply blacklist your AppleID for several services like iMessage or Facetime.

This blocking/blacklisting mechanism seem to work in two directions since you´ll still be able to use iMessage or FaceTime on a genuine Apple Device with your AppleID but will be blocked on suspicious Devices. All genuine Macs get registered with Apple the first Time they connect with the Internet and get associated to an AppleID once the iCloud Service ist activated or the AppStore ist used. In the process of registration the Apple Servers check if the transmitted values are plausible or not. At least they check wether the given serial number matches with Apples databases or not. In case it matches they check whether this machine is already registered with Apple or not in case it is already registered they also check if the stored MLB and ROM values fit the submitted values and if they fit you art good to go if not you´ll be able to use iTunes, iCloud and the AppStore but will be blocked for iMessage and FaceTime. It´s that simple...

But there´s also a whitelist some really old AppleID´s seem to be on this whitelist (mine is one of them) except of Apple themselves nobody knows why this ID´s are whitelisted and what has to be done to become whitelisted but once whitelisted you´ll be able to login to iMessage and Facetime even if no values are transmitted or common Values are used (e.g. standard values set by Clover or Ozmosis). Actually the only way to get iMessage and FaceTime to work is to clone a real and with Apple registered genuine devices values on your hackintosh preferable the values of a device which isn´t in use anymore.

And @Sofista please do me a favour stop opening new threads or hijack old threads for this issue since all was could be said about it is said right now.

If you have or get aware of an old genuine MAC which is no longer in use just use the values of this machine since it is registered with Apple. All you need to do is to run the iMessageDebug Script on this machine and carefully write down all of it´s output. Disconnect your hackintosh from the Internet and change it´s SMBIOS according to the written down values from the genuine Machine. You´ll need to change the serial number, the MLB Value (BaseBoardSerial), the ROM Value and the HardwareUUID value. Once done reboot your hackintosh run iMessageDebung Tool on it and double check if all Values match the ones taken from the genuine device if so connect it to the Internet and logon to iMessage and Facetime it should work now...