Reason 1. It violates GAR #27 - Freedom of Assembly.
Clause 5 of the proposal makes it illegal for Religious Institutions to involve themselves in politics.
I think this violates Clause 1 of Freedom of Assembly says "All individuals shall have the right to peacefully assemble, associate, and protest to promote, pursue, and express any goal, cause, or view", which gives any group (regardless of the type of group) the right to assemble to express a view. If a religious group wants to assemble to endorse a candidate, its right to do so is protected under this Clause (providing they do so peacefully).
Reason 2. It violates GAR #155 - Freedom of The Press.
If a newspaper's primary function can be described as religious (an example could be The Watchtower) then arguably it would fall under Clause 5 of this proposal.
Article 2, Clause 5 of GAR #155 forbids censorship of newspapers under any circumstances (except national security, which I do not see this could be classified as), and if a newspaper is not free to endorse or comment on a political campaign because of this new proposal, then I believe it would be an act of censorship and a violation of this clause.
There was going to be one more, but the proposal has been edited since the last time I looked at it