It is important to pay attention to who you are talking to, no matter what you want to say. If you are aware of the culture of those you are communicating with, you can avoid confusion. You can also be sure that your audience will not be offended by what you say. Neither is conducive to good communication.
Speakers have to take an audience centered approach in order to meet the needs of the audience. I have heard the same speaker with the same general topic but giving it to different audience. The message was the same, just the presentation was different.
All excellent points. Think for a moment of any time you;ve been in the position of audience when the speaker wasn't particularly attentive to his or her audience. I'm sorry to say I can think of church services, classroom lectures, teacher workshops, and other types of events I've attended which I only remember because they were poorly presented or poorly prepared for the given audience. If one wants to be remembered and even repeated, one must be relevant. How better to be relevant than to meet the needs of the audience to whom one is speaking. Audience matters in every communication, from conversation to formal lecture, from text to treatise.
Without a specific audience in mind, your purpose can not be entirely clear. Without a clear purpose (entertain, inform, persuade, etc.) you lose focus in the writing, speech, etc. Of course, then, no one will read or listen, thus making the entire process a moot point.
If the author isn't clear on his or her intentions, the writing will also be unclear and obtuse. It will wander and be prone to tangents that do not support anything. Therefore, the audience will not be reached.
I think an author or speaker who cannot identify with their audience will not only be moderately successful, but more like ineffective. Without connections to their interests or language style, the message can be lost. For example, if you went to a bunch of teenagers and spoke as if you were a business executive, they would have little concept of the language you used or the purpose for your dicussion with them.
To respond to the second part of your question, cultural context is of course vital for communication. There are so many examples of a speaker not modifying or thinking through the cultural context of his audience and getting into all sorts of difficulties because he or she doesn't understand how his audience views the world and the topic he is speaking about. One example that comes to mind is Boris Yeltsin's wife visiting earthquake victims in Armenia dressed in a hugely expensive fur coat. Even before Yeltsin had opened his mouth, his audience was against him because of their poverty and crisis situation. Again, consider an adult speaking to a group of teenagers - the adult would need to know bits of information about their lives like what kind of music they like etc to make his message hit home.
The purpose of communication is to reach an audience, to communicate a set of ideas, right? So if it is not an audience-centered approach, we greatly reduce our chances of the message reaching the audience. In both teaching and in professional presentation, a more active and engaged audience is central to learning.