Interestingly, when I've asked this question before, there has been some argument. No, not on whether the customer is more important (most everyone seems to agree on that), but rather on which customer is more important - the client you're designing for or the customer of the website you're designing for the client. When I say customer-centered design I'm not talking about the client. But I do recognize that clients can have vastly different desires from what their customers do, and if you're a freelance designer, serving your clients first is an easier way to keep them paying you. But as SazBean points out in their article Customer-Centric Design - Your Customers Care, so Should You:
Your goals are probably concerned with increasing sales and leads (if not, they really should be).If you reinterpret this as "Your goals should be concerned with increasing the sales and leads of your clients." Then you'll have a handle on how to work with clients who want pages with black backgrounds with white 8px type for their audience of senior citizens.