These religions are run no differently to any other lucrative business or powerful political party.
I have seen some of the poorest villages in the Phillipines (where people cannot feed their own family) have wealthy local churches because everyone is essentially 'encouraged' (guilted/manipulated) into donating. It sounds silly but the more desperate your life, the more you feel the need to donate to this almighty presence. After seeing the amounts collected and seeing the sheer vastness of wealth in the Vatican as a kid, i realised that religion=business.
So does it have the right to advertise? Yes it does but theatres are well in their right to refuse. It is a business for the cinemas too and advertising costs just supplement the business made from the films. If they wish to avoid alienating customers who are simply not interested in the CoE or they think the advert will have an undesirable effect on the mood of the crowd, then it is in their best business to refuse the CoE. If they have to give an excuse then their policy of not allowing adverts with religious or political connotations, then that is fine. People seem to be more offended by their refusal because they think its some crazy plan to appease minorities, when in reality, its just bad business.
I think CoE reaction is in poor taste and is further proof that all of this is just business. Raving on about the refusal has given their advert tons of publicity for free, at the same time putting negative connotations on the cinemas refusal.
From a cinema point of view, if they accepted CoE but refused to show Islam/Mormon/Etc adverts then it would seem like they have some affiliation with them, where as they want to appear neutral. If they accepted all adverts, then it will eventually hit a nerve with the crowd and business goes bad. With that view in mind, it as about not wanting to offend Christians as well as Non-Christians.
If I went to the cinema and say a 1 minute advert of Nigel Farage pretending to be my pubs local while shouting about taking the country back, i would be pretty put off my film.