No, employers cannot do whatever they want.

I've seen some attempts to defend the "right" of employers to infringe on the rights of their employees because those employees, after all, can quit and find a new job.

We have in fact already fought this battle, and it is already established that an employer cannot do whatever they want to their employees.

They can't pay women less.  They can't discriminate against minorities.  They cant sexually harass their employees.  They can't force them to work 100 hours per week or force them to go without lunch.

I could go on.  This fight has already been had.  It's unbelievable to me sometimes how much perspective and sense of history Americans can lack when having a political debate.

The end result is Americans completely lose the ability to approach things in a balanced way.  Nobody is going to make priests hand out condoms.  It doesn't follow that employers can do whatever they want.  Sheesh.