I suppose first and foremost is the idea that a company has a religion- the owners themselves might, but the company does not, so there goes any ridiculous religious freedom argument. Never mind that in the pursuit of their "freedom" they're trampling on the rights of their employees, specifically the right to control their own body by what their morals say is appropriate. But that seems to be a common theme these days, doesn't it? Women are idiots incapable of making our own healthcare decisions especially when those decisions might run counter to our being anything beyond breeding chattel for rich white men.
Then there's the science, or rather complete lack of, present in their arguments. Birth control of the sort that they're talking about does not cause abortions- all of them work by preventing implantation of a fertilized egg. Oh, but life begins at conception, you say, at that magic moment when sperm meets egg? Then lets talk about the biggest abortion provider out there- nature. Or God, in the minds of these people. Depending on the study you look at, somewhere between 30% and 50% of fertilized eggs never implant in the uterus and simply flush out of the body with the regular menstrual cycle. So god can prevent up 50% of pregnancies, and that's ok, but a woman isn't allowed to make that decision herself.
What about after implantation, when the medical community starts to consider it a possibly viable (and detectable) pregnancy? I'm going to quote straight from the Mayo Clinic on the dangers of taking Plan B if you're already pregnant meaning that implantation has occurred.
if you're already pregnant when you take Plan B One-Step or Next Choice, the treatment will simply be ineffective and won't harm the developing baby.
Plan B One-Step is not the same as RU-486, which is an abortion pill. It does not cause a miscarriage or abortion. In other words, it does not stop development of afetus once the fertilized egg implants in the uterus. So it will not work if you are already pregnant when you take it.
In short, Hobby Lobby, and anyone else who thinks they should be able to control the health of women, can just shove right off and find some actual facts before they start trying to legislate their ideas or get exemptions from existing legislation.
And if you still really think it's anything to do with protecting "babies" rather than controlling women, take a look at this article. How I Lost Faith in the "Pro-Life" Movement."
*Note that this only includes 1st trimester losses, anything after that falls under the heading of still birth rather than miscarriage.