Healthcare is a service. It has to be paid for somehow. If government is saying someone has to provide a service with or without payment, then that means that paying customers have to cover the expense somehow. In the meantime, what if the only provider available in an area doesn't want to provide the service? If it is government enforced, that is coercion.
In short, the policy is state coercion if the provider of care would normally refuse service.
That is a real stretch.
The only things you are being "coerced" to do, are to pay your taxes and abide by the law.
What the government does with each and every tax dollar they collect is not a matter for individuals to have a say over, nor should they, as the government is under no obligation to check with each and every individual citizen to get permission for what they do with our taxes.
That is why we have elections and representative government.
There are things the government spends our taxes on that I don't necessarily like or approve of, but to say I am being "coerced" to pay for them would be hyperbolic.
As for your question about a medical provider not wanting to perform medical care on certain people, that provider would be in violation of their Hippocratic oath and subject to disciplinary action or possible loss of their licence.
Of course, if you were thinking about a reluctance to provide an abortion on moral grounds, only abortion specialists normally perform abortions, so that would be a moot point. And a general practitioner would not be required to perform an unnecessary, non-emergency surgical procedure anyway. So again, moot point.
If one doesn't like something that's being done with our tax dollars, one may begin a grassroots movement to challenge it. Keep working until their grassroots movement expands nationwide then elect those who will undo whatever it is that they dislike.
That, in theory, is the way it's supposed to work. Whether it does in practical terms or not is debatable. But really, what we have is the best and only way it can be.
