Personally, I thought the crux of the issue was that corporations are allowed to express "religious affiliations" and impose them on their employees. I saw it more as the broadening of corporations' rights, and the very phrase "corporations' rights" feels wrong to me. I do not believe a corporation should have the same rights as a person. To me in a way that then allows a corporation to become a personhood monopoly especially when they are then allowed to impose their views on their employees. "We have the rights of a person but we employ thousands of people and we can now refuse to grant certain services to those people." Despite what the rights of those individual people are supposed to be. It's like, due to employment by a corporation, the corporation's rights can then supercede the rights of their employees.
To be truthful I think my comment essentially takes a line out of yours and expounds on why that's problematic in my mind. It's this part I find interesting and would like to hear more about your opinions on if you want - I feel like I don't have the knowledge or context to provide commentary on this issue: 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'.
I can't articulate nearly as well as this, so why try? Edit: I should really temper some of my language. Although 'originalism' is the rallying cry of the extreme Right, this isn't a constitutional case. It's actually a statutory case, which interpreted the Religious Freedom Restoration Act to get the result. An act of Congress could, therefore, overrule this decision.