So much for freedom of conscience. This isn't necessarily a religious debate. There are those that aren't believers but think this is murder.
Does a cashier who opposes drinking have the right not to sell alcohol to customers?
She absolutely has freedom of conscience. Being fired from a job doesn't touch that.
What she apparently does not have, however, is the right to determine what she will and will not do while on the payroll of Target.
You are absolutely right that this is not a religious debate, nor does it really have anything to do with the morning after pill. It is about her employer requiring something of her, and her refusal to comply.
Employment at will is a 2 way street.