From the information below it seems this law is aimed at Islamic groups as well as non-registered Christian groups, such as the Jehovah Witnesses and (probably) certain Baptist groups. And my guess is that it won’t apply in the same way to Orthodox Church services or public displays.
NOT IN ANY WAY APPROVING - such clarifying that the aim of the law is broader than Christians.
http://www2.stetson.edu/~psteeves/relnews/160706a.html
The purpose of this law is the same as Communist era anti religious laws, speech codes on campuses, and other laws that restrict speech, debate, or criticism, religious or not.
They are intended to restrict and shape public discussions in ways that benefit elites, the establishment, or favored groups.
In Russia’s case the Putin government and his tame church (I admire Orthodoxy as faith, but not the Russian Church’s alliance with Putin). Government sanctioned religion is never a good idea.
This is little different than campus leaders restricting Christian groups and permitting Muslim groups special considerations, and creating “safe spaces” free of dissent. It is not the job of government to take sides for or against religions, ideologies, ethnic groups, etc....