There is no federal tax reason why a charity must refuse a contribution from a church or other religious organization.  It is possible, though probably unlikely, that there is a restriction in the charity’s governing documents.  It is more likely that the charity simply has a policy of not accepting gifts from churches, like some foundations have a policy of not making grants to churches.  If that is their policy and they are willing to live with the bad publicity, there probably isn’t much that can be done about it.