There is nothing I can say, no matter how true, that will change your opinion.
Well, you can imply that I have a developmental disability and change my opinion of you.
Apparently there's nothing that biologists or Catholic bishops can say, no matter the actual evidence, that will change some people's opinion that Plan B causes an abortion.
Your perspective is that of what you want to see.
True. Let me tell you what I want to see. I want to see a world where everyone is free to believe whatever they wish, and freely express those beliefs. I want to see a world where my employer has zero control over my health choices.
Let me also tell you what I do see. I see a culture where employers provide medical insurance. I see a market where medical goods and services are paid for by insurance. I see a law that defines a certain minimum acceptable insurance coverage. Now, I don't particularly like the implementation of these three systems; I'm just saying what I see.
The most elegant way to reconcile what I want to see with what I do see is to assert that the employer's influence ends when their money reaches the insurance company. The insurance company defines coverage to meet or exceed the requirements of the law. The legal minimum should be treated as an indivisible unit; the employer is not allowed to choose a policy covering less than the legal minimum, therefore the minimum can be purchased without making any moral judgement. The employer is free to choose to offer whatever extra coverage they want as part of employment contract negotiation. They can make whatever moral judgements they like about cosmetic surgery or chinese medicine.
Some employees will use their insurance benefit to treat endometriosis with hormonal supplements. Some employees will use their insurance benefit for fertility treatments. Some employees will use their insurance benefit to prevent pregnancy. Some people would never use any of these because it violates their religious beliefs. That's fine; the beneficiary of the policy gets to choose what the benefit is used for. The payer of the policy has no moral skin in this game. If the beneficiary fraudulently obtains prescription drugs and sells them on the side, the payer did not buy or sell the drugs and has committed no crime. If the beneficiary legally obtains contraceptives and uses them, the payer did not buy or use the pill and has committed no act of moral depravity. To claim otherwise is to assert that the payer's moral and religious views supersede those of the beneficiary.
Imagine that Hobby Lobby chose to renegotiate all their employment contracts, no longer providing health insurance but paying a higher salary. This salary difference is contractually constrained to the purpose of purchasing an insurance plan. The model remains the same as I described before: Hobby Lobby pays the insurance company, the insurance company puts that money in a pool, the employee spends their allotted insurance benefit. The only difference is that Hobby Lobby didn't choose the plan. The only difference is the amount of control Hobby Lobby has over the employee's health benefit. It is dissonant to assert that Hobby Lobby pays for contraception when in fact they pay for insurance. It is abhorrent to allow Hobby Lobby to withhold the legal minimum insurance coverage from their employees due to a perceived coercion to violate religious beliefs, due to Hobby Lobby's faulty models of how insurance and contraception work.
The fact is, Hobby Lobby employees don't ask Hobby Lobby to pay for their heart surgery. They ask Hobby Lobby to pay for their insurance. They ask the insurance company to pay for their heart surgery. The insurance carrier doesn't hold Hobby Lobby's payments aside to only pay for Hobby Lobby employees. It all goes into a shared account. If any beneficiary covered by that insurance provider uses their benefit to buy contraceptives, Hobby Lobby's ex-money effectively pays for part of it. Hobby Lobby's ex-money will go on to support war, illegal drugs, legal drugs, rock concert tickets, and political bribes as it filters through the system. What happens to Hobby Lobby's money after they spend it has no bearing on, and should have no influence from, their beliefs.
Quakers don't get to pay half tax because they sincerely believe in pacifism and don't want to support the military budget. But even if they could pay half tax, the government doesn't reduce the military budget based on conscientious objectors; they collect everybody's tax money in a stream and then divide that stream. That Quaker's half tax effectively gets halved again: a quarter of their original tax obligation goes to the military anyway. With every breath you breathe Feynmann's ex-air; with every purchase you spend Feynmann's ex-money. Hitler's too. Morality, and expression, stop at the edges of the shared resource stream.
I understand that the court decision is more subtle than this broad view. I think the non-profit exemption that this decision hinges on was a bad idea in the first place, ceding to other employers who also clutched their pearls, in effect worried that they didn't have enough control over their employee's choices. That law and this decision come down to allowing employers to say "Even though my belief is based on zero evidence, I sincerely believe it and therefore you have to go through extra effort and expense to receive the legal minimum health benefit."
The rule exempting religious nonprofits from having to meet the legal minimum insurance coverage should have been ruled unconstitutional here. This exemption prohibits the free exercise of the beneficiary's religion, by allowing an employer's religion to be exercised in its place. The legal minimum coverage does not prohibit the free exercise of the employer's religion; the employer remains free to choose whether or not to buy or take a contraceptive into their own body. The first amendment does not give anyone the right to exercise their religion in someone else's body, only their own.