When you're in business what is your responsibility/responsibilities to your customers? Why?

What business?  If you accept someone's money, they are your customer.

If you turn down a customer, you are probably in the clear until you accept the money.

If you give bad customer service, you won't have a business.

Whether they paid or not.

Give them what they paid for and do your best to make sure they are satisfied. 

Sometimes I turned customers away. I had a seasonal business and they would have major jobs that took too much time.  Everybody wanted ME to do all the repair work. It was frustrating, and so I gave it all up.

Your responsibility is that of contract. If you don't take care of some needs in the community, some people might refuse to contract with you. Both you and your customer base are free to do business or don't. I mean back when we lived in a free country. Not now.