You used: "If an Amish individual took a job in an IT firm and claimed a conscientious objection to using modern technology, I don't think they'd get very far." But really the more apt analogy is that the Amish hire someone who is not Amish to say, feed the pigs. If they then say, "We'll pay you for this but you can't use any of the money to buy technology like an iPhone or television." THEN you've got the analogy.
Health insurance is, effectively, part of the payment that employees get for their work. I mean, really, is the Catholic Church any *less* paying for contraceptives if a woman uses her salary to buy it? Is that the next step? The Church saying, "You can only use the money we pay you in ways we approve, no matter what you personally believe"? Putting it another way, if the Amish provide health insurance to their non-Amish employees, they can't say, "We'll won't pay for health insurance that allows our employees to be X-Rayed or given ulta-sounds..." Once they give the employees heath insurance--like giving them money--what the employees do with it (i.e. what their health requires they get with it) is not up to the employer. It's up to the employee and his/her doctor.