I completely agree that anything said on social media (Facebook, Twitter, internet, etc.) is in the public realm and no longer a “private conversation” but let me ask this. This woman was an apprentice to a Christian Chaplain so her views should have been anything but surprising. So how is expressing a view that is in total agreement with the job she holds a violation of anything?
Even the views as she expressed them were not offensive.
There doesn't need to be a violation of any policy for there to be disciplinary action. I've signed no contract or agreement to not shout the 'N' word at customers, but I'd
expect to be fired for that action. When it comes to whether or not this was in "total agreement" of her job, she was out of that agreement the second her employers say she is. "Offense" is in the eye of the beholder, and the only one that matters is the employer; if they hadn't been offended, we wouldn't be discussing this right now.
Whether they were really offended or not is kind of immaterial, as well. An employer can discipline you for any reason that isn't protected by law, and Facebook posts aren't protected by law (barring privacy laws, which only apply if they "forced" her to show them a truly private conversation).
Your analyses of the law seems accurate AFAIK and show why we need a federal law protecting employees rights to privacy and free expression. Something like this:
Employers, including federal, state and local government, may not discriminate against, or discipline any employee for their off-duty activities, whether public or not, unless the employee explicitly represents his or herself as a representative of the employer as part of the activity, or the employee has been convicted of a crime related to the activity. Employers may not be held responsible for the off-duty activities of employees unless the employer specifically requested or authorized the activity as a part of the employee's duties.
Without such a law, we are all in danger of losing our first amendment and privacy rights to our employers.
Note that this law would benefit employers as well as employees because it would protect them from any legal consequences and liability for their employee's activities. When an employer is embarrassed by an employee' activity they will be able to honestly say that the law prevents them from doing anything about it.
That would protect employees from doing plenty of stuff that you'd never support; yelling/cursing at customers (not a crime or their duties), getting drunk as a skunk the night before (not a crime or their duties), posting truly derogatory/offensive/threatening rants about co-workers/customers/employers/etc. (absolutely necessary to preserve a safe working environment), screaming the 'N' word in the parking lot just before a shift, etc. There are plenty of things that absolutely shouldn't be protected, that would be under that law.
People should be protected from airing grievances, and most employees are. There should be no "force" to make an employer keep employees that disrupt business. I fully agree that PC has gotten out of hand but, these posts obviously offended coworkers before it got to upper-management; that's all that's required for a lawsuit, so that's why an employer would cover themselves by taking disciplinary action. The only people that would benefit from this proposed law would be bigots and morons; I doubt you would like the new world it creates. People have always been taught to think before they speak, and they shouldn't be protected for doing the opposite.
When it comes to protecting our first amendment and privacy rights, I say they are already protected; you have always had the right to say anything you want, including now, and you've never had the right to keep your job if you offend people, including now. Your rights are just as strong as they have ever been. Privacy is also protected; an employer can't legally force you to show them your social media accounts. If you inadvertently offend someone by your posts, it's self-evidently not a private conversation, or they couldn't have known what you posted. It comes down to ,watch what you say, who you say it to, and don't say anything if you can't do the first two. That's a universal law of common sense, and people shouldn't be given legal protection for having no common sense.