Claims based on the fact that God is mentioned in the constitution are bizarre, to say the least. Is there any part of the constitution that then goes on to state (or even imply) that those who do not believe in God shall not be entitled to benefits, rights, protections, etc. in said constitution or other law? If there is not, then the matter can be settled in a simple and straightforward matter:
The registration of societies is regulated by certain laws that are not particularly hard to understand. A decision on whether or not to register Godless people can (and should be made) solely on whether they comply with the relevant laws and regulations. As the law currently stands and is understood, the groups that may be denied registration are those that pose a criminal danger to society. For example, a Rapists-and-Murderers Society of Kenya may (and ought to) be denied registration on the basis of the unsavoury nature of its primary activities.
Amicus Mortician knows the law, but he has a "job" to do: there is an election coming up, and the Jubilee government doesn't need the churches making unhelpful noises.