As an employee you can either do as asked or quit.
Uber Eats is a service that connects you to a contractor. The contractor may at any point decide they do not want to work for you. That ends their obligation to you and yours to them. It is that simple.
But I am quite sure that if the reason for denial of service was due to the customer being part of the protected class then such could be prosecuted as Jack Phillips (Masterpiece bakery) was and is for years.
Of course, including a class of persons thus protected on the basis of how they feel and act, versus non-moral aspects such as race, color, ethnicity, nat'l origin, and or being part of a recognized religion (which loses when the conflict it btwn the two), was unprecedented, and opens the door for inclusion of other classes based upon feelings and behavior.
Maybe the Uber driver can claim that his opposition to contraception was due to him/her being "born again" that way...