The doctor in this article is wrong just as the florist was in the other topic. Which is the sin? Providing a service for someone even though they may use it in a way that is against your religious convictions that there may be a future opportunity to reach them with the Love of God through the Gospel; or, refusing a service because it may conflict with your religious beliefs and lose any possible opportunity to show them the Love of God through the Gospel?
If God's justice was more important than Love we wouldn't even have the Gospel of Jesus Christ to share.
The unregenerate sinner will always find a way to sin with or without the flowers, with or without the doctor caring for their child. when a service is refused as in this OP all it does is close the door on an opportunity to share the Love of God through the Gospel.
If God could love us despite our sinful condition and send His Son so that we may know that love, how can we refuse to serve others in order to show them the same love that was shown to us?