The idea that employers have a right to impose their religious beliefs on their employees should make anyone who actually believes in freedom of religion puke.
It's slightly more nuanced than that. If you run an insurance company you have to be responsible for the pharmacy formulary (deciding which drugs will be covered under the insurance plan) and the list of covered medical services and procedures (ER visits, well-checks, mammograms, abortions, caesarian sections, chiropracty, heart surgery, plastic surgery, gender re-assignment, etc.) that will be covered. Suppose you have a moral or financial objection to plastic surgery, which isn't too uncommon for insurance companies. Most insurance companies will not cover elective cosmetic procedures unless it's to treat an injury. This is an ethical/moral decision on the part of the insurance company; they believe that enhanced physical appearance is not important enough to the insured to cover fully. It's a very similar argument that a few insurance providers use to not cover contraceptives and abortion, and in general they should be free to cover whatever they feel is appropriate and the market should decide which insurance companies prosper.
The first problem occurs when restrictive insurance providers also force their employees to use the insurance they sell, which effectively happens any time an organization opts for medical self-insurance. The second problem is when the government requires all insurance providers to provide a basic level of service and forces entities to cover medical procedures or drugs that they don't think are morally acceptable. Both problems are infringements on free choice and the free market, but the latter is definitely closer to what the civil rights act prohibited, e.g. a correction of attitudes and beliefs that are just wrong and harmful.
I think pretty much every employer would prefer not to be involved in health care. It is a stupid system. But the reason that it was necessary is that insurance does not work when the insurer knows the individual risks. The individual insurance market began to collapse in the 1980s.
It's actually surprising that employers don't do the same screening that individual insurance carriers do and refuse to hire high-risk employees, since that would greatly lower the cost of self-insurance. Maybe the ADA prevents it? The closest example I can think of are campus smoking bans which effectively fire or cure employee smokers. Maybe campus fatty bans are next.
I agree with you that some sort of mandate is necessary so that everyone can be insured, but I am not enough of an expert to know what makes sense to mandate. Mandating that every medical procedure and drug including cosmetic surgery and off-label experimental use must be covered would be going too far, and mandating only that insurance had to pay for one clinic visit a year and up to $10,000 per ICU stay would be too limited. Driving some insurance companies out of business because they can't comply with the mandate is probably the lesser harm, but it is definitely a harm if employers/employees have to pay more for equivalent insurance elsewhere. For one thing, there are presumably people who want to buy insurance that matches their ethical standards and if the buyer and seller of the insurance aren't harming anyone else I don't think it's right to interfere. Clearly, only if an employee can freely choose the insurance they want is a requirement for the preceding to be true. It would be too easy for employers to make employees a deal they couldn't refuse otherwise.
The only way to get the ACA passed though was if people who already had insurance were assured that they wouldn't lose it. Many people have subsidized insurance built into their employment package and would lose substantially if that happened. Which is why the ACA has big tax penalties for employers who drop coverage and requires the coverage to meet certain minimum standards.
Perhaps if the tax loophole was changed so that employers could only pay the subsidized insurance cost directly to employees for use in purchasing their own insurance, there would be an incentive to make insurance marketable while getting employers out of directly providing healthcare. I haven't read the ACA directly, so perhaps that's the ultimate goal with the individual mandate.