Government is ordering people to DO something they don't want to do.
Government is ordering health insurance plan to insure health services.
If there were a health objection, that would be one thing.
But there isn't.
If female contraceptive services weren't considered part of health care, you might have an argument.
But when you're running a health care company, you have to deliver health care.
Beyond that, the government orders lots of people to do things they don't want to do.
Such as pay taxes, and serve on juries, and pay child support, and register with the Selective Service.
I am cheering for the absence of coersion
No, you are not.
You have no problem whatsoever when an employer or a church coerces a health care decision.
It's only when the government stands up for a woman's right to access modern health care that would be denied her based on religious superstition that you cry "coercion!"
But in truth, it's always a trade-off. So let's say both ways are coercion. Maybe a good way to judge which is preferable is to look at how many people are being coerced. On the one hand, you have potentially millions of women losing access to contraception. On the other hand, you have a handful of corporate fictitious persons being told they are required to process certain billing codes used elsewhere in the industry.
I can tell which of those scenarios coerces more people. Can you?
Think it through, Murphy.
I admire your optimism!