- Both "be angry" and "get angry" are valid English constructs, and can have different meanings depending on the context.
- "someone whom you are disagree with" is wrong. Your second choice-"someone you disagree with" is the correct one.
Coming back to your first question:
You can not "be" angry while listening to [...]
This sentence implies that you should not already be angry while listening to someone you disagree with. It's sort of a continuation of your anger from a previous instance, if you will.
You can not "get" angry while listening to [...]
This says that you should not "get" angry when listening to someone you disagree with. Here, your anger is implied to arise out of the conversation you have with someone, and not as a previous continuation.