I am assuming from what you said that you are the lowly peon caught in the middle of the communication mess and who is getting the "carp" flowing down hill. ( (((HUGS))), been there, done that, didn't buy the t-shirt because I wanted to forget. )
You need to get clarification about from your immediate supervisor. You are getting flack because managers cannot be professional and communicate with each other. I would ask your supervisor what protocols you should be following with each situation.
If Department B manager gets upset with you not communicating what Department Manager A said, ask your supervisor what the communication protocols are that you should be following. Should you copy Manager B on all communications sent by Manager A? Should you ask Manager A if this has been communicated to Manager B? Once you have the protocols, follow them to the letter.
If Manager A doesn't want his/her communications sent to Manager B, as per protocol you are told, then point him or her to your supervisor for clarification of protocol.
Who is responsible for communicating policy changes in your company? I have never heard of a peon telling managers about policy changes. That is a top-level down communication in every company I have ever worked for. Even HR changes are communicated by same-level HR managers to department managers.
The next time a manager gives you a policy change to communicate, take it your immediate supervisor and ask for clarification. Even if you are the one to communicate it, there needs to be something indicating "Manager A requested I send this policy change out to everyone in Departments A & B."
It is a mixture of professionalism and CYA. You get a clear protocol from your immediate supervisor which you follow. You document everything so when the "carp" starts flowing you have a natural dam for diverting it to the people who deserve it.
Every newcomer has to learn the office culture. When dealing with a culture as dysfunctional as this one, you need to keep things professional and always ask for clarification in odd situations. By making your immediate supervisor aware of it and getting clear protocols, you may start to see some changes. If it doesn't change, you might want to consider a new job or a transfer.