The whole premise here is false.
I have yet to see an employer that objected to the most common forms of birth control. So it would help to be a little more honest about what is going on there. A handful of employers object to some very specific forms of birth control because they believe them to be equivalent to abortion in some respect. We can agree or disagree with that stance. Though if I was a woman employed at one of those companies I would be asking for an increased salary if the value of my health insurance was reduced. If not they are lowering my compensation.
Women are capable of getting birth control absent coverage from their health insurance. Its just that if their insurance used to cover it and now it doesn’t they have more out of pocket costs. Their employer should pay them the additional money that would have gone to the insurance company as a wage instead. If the move is based on their moral convictions rather than simply saving money that shouldn’t be a problem.