Well, she certainly didn't read the decision, which explicitly discusses this argument, and says that the point is not whether these pills cause abortion but whether the business owners' religion believes they do.
But the decision likewise doesn't say "that government should not be able to coerce you into going against your religious beliefs," only that they can't do so without a strong reason. Otherwise, I'd start the "It's a Sin to Pay Income Taxes Church" and have 10 million converts by next Tuesday.
Well there is kind of a group like that, it’s called going Galt.