That's a good question. I think that the issue isn't women being denied contraception. The issue is that of specific religious ideologies being imposed on society as a whole in the name of religious freedom. Here's what I had to say in a comment the other day:

1) The ACA is a tax (according to the Roberts Court)

2) Money is speech (according to the Roberts Court)

3) Religious exceptions trump the paying of a tax (according to the Roberts Court)

So it doesn't take a genius to make the next leap. That is, how can anybody be forced to pay any taxes now, given that almost everything the Federal Government does is offensive to someone's religious beliefs? If I'm a Christian Scientist entrepreneur, can I simply not pay for any health coverage? If I'm a Quaker, can I refuse to pay the portion of my tax that goes to DoD? And so on.

Ah, but I suspect not. I think a far simpler explanation is that these extreme right wing Catholics who make up the 5 member majority on the Court are letting their ideology control national policy just a tad too much, eh? Remember back in 1960 when JFK had to give a big national speech assuring mostly conservative voters that he wouldn't let his Catholic faith or his allegiance to the Pope trump national interests? Well that got flipped on its head sometime in the last half century. It's a joke (unfortunately, a joke of which we're all the butt) that this is all done in the name of originalism. Separation of church and state is dead, flat out dead.

This decision is less about women's rights than it is about the further degradation of the separation of church and state. Scalia and Thomas especially seem hell bent on merging a specific version of Christianity into the fabric of the Constitution, and all in the name of 'originalism'.