So it ends up basically being the same as the whole civil rights thing. There's a point you can't deny service to someone based on their skin color, and there's a point where you're allowed to express your beliefs. There's a point where you can't force someone to provide services they disagree with, and there's a point you can do so. It's like the same thing, just fast forward 50-odd years.
I disagree. There's a massive difference between the government saying "If you provide Service X, you must provide it to all customers who walk through your door regardless of gender, race, etc." and "You are required to provide Service X". The former is about discrimination against individual (or groups of) people and can be justified as a rights issue. The latter isn't about rights at all (except the infringement of the rights of the provider).
If we start with the assumption that we all innately have the right to control how we use our own property (and we should, since that's a core concept of liberalism), then we should conclude that the government can only infringe this right if there is another competing right which outweighs it. In the case of discriminating against customers of a good or service based on their race, gender, or religion, this is pretty clear cut. And in the case of discriminating against employees (for hiring, pay, or advancement) based on those same criteria is also pretty clear cut. But what is the competing right which requires that a business provide a good or service that they don't want to involve themselves in at all? Even to their own employees? If they say "this is the benefits package which all employees receive", it's not discrimination. They aren't saying "white folks get these benefits, while black folks get a different set". Every employee gets the same benefits, so there's no discrimination.
Ah, but you say: But isn't refusing to provide contraceptive coverage a discrimination against women? Not really. Discrimination has to be viewed in a direct manner. Do male employees get a better deal than females? It's not such a clear issue, given that men and women have different health care needs overall. There are numerous differences and we could probably go crazy trying to bean count them all. Plus I suspect that if we did bean count, we'd find that women tend to get a better "deal" overall from health benefits than men. Also the issue of spouses and dependents further muddies the waters. Point being that you can't really point to a clear discrimination against a given group of employees in this case. Certainly not one that outweighs the infringement of the business owners innate property rights.
The irony here is that the ACA mandates actually create a good portion of the problem. By forcing employers to provide health care benefits (and/or forcing everyone to purchase the same via some methodology), the government is actually putting employees in the position of having to "pay" for health care that may not exactly match what they need. For example, prior to the passage of the ACA, an employee was free to opt out of the employer coverage and use the difference in funds to purchase just the insurance he/she wanted (or none at all, pocketing the difference). Most wouldn't, because you could usually get a better group rate going through your employer, but the option was there. I'm not sure how much harder the ACA has made that choice (and it's absolutely eliminated the "no care at all" option), but this is more tricky to do than it used to be. Certainly, the employee will find that the mandates on coverage will ensure that there are fewer choices out there.
Point being that prior to this, you could have chosen to purchase just emergency coverage and pocketed the difference to use to directly purchase any form of contraception you wanted. Now, you either get it with the coverage, or you have to pay a greater cost out of pocket for the same thing. It's a matter of degrees, of course, but if buying contraception directly is a financial burden, then odds are this change is impacting you negatively. And that's the real problem. The ACA reduces the freedom of choice of everyone involved. That's the problem. This particular case is just one effect of that problem. There are many many others.