The Supreme Court decision about the Affordable Care Act (a.k.a ObamaCare) found that the individual mandate to have health insurance is a tax, which congress has the power to impose. It is not a stretch to look at the employer mandate as a tax as well.
We have long since established the principle that a conscientious objection to some of the uses of tax money does not entitle a taxpayer to refuse to pay. For example, the Society of Friends (Quakers) are pacifists, yet they are not excused from paying taxes that support the military.
The Supreme Court decided in the Citizens United case that corporations have some of the civil rights of citizens, including, I suppose, the freedom of religion. However, there is nothing to support the proposition that citizens' freedom of religion entitles them to decide which taxes they wish to pay.
What would be the consequences of allowing corporations to choose which health benefits it offers? Could a corporation owned by devout Christian scientists claim exemption from the whole law, on the ground that they personally don't believe in medical care? We don't allow parents to deny medical care to their children in dire cases, even if the reason is religious. Why should we allow corporations to deny support to their employees because those employees make personal health choices that the corporation owners regret?
I deeply respect the choices of those who decline to use birth control, to have an abortion or to participate in a marriage between two persons of the same sex. That is their religious freedom, and I support it strongly. But those choices do not entitle a person or a corporation to refuse to pay their taxes.