Let's think about a Muslim slaughterhouse to see how this is a false dichotomy.
A Muslim slaughterhouse can refuse to slaughter pigs. However, they can't just refuse to slaughter pigs that belong to Mormons.
A black or Jewish printer can have a "no racist posters" policy, and deny racist posters. The KKK members could still have non-racist things printed. (ignoring the fact that KKK membership isn't likely to ever be a protected class).
Similarly, a person can have a, "No gay cakes" policy, and still have to sell a generic, "congratulations" cake that they normally make.
And a pharmacist can choose to not dispense certain drugs, and then be fired by their pharmacy because of refusing to do their job.
tl;dr - There's a difference in refusing to do certain things and refusing to serve certain groups of people.