Manager emails a list of employees who have not yet completed a training module. Is this a labor violation of any kind?

I know that this tactic is immoral and represents weak leadership. The use of shame and humiliation is never the right answer to any problem.

Maybe my take on this one is weird but I don't think morality has a part here, nor a definite signal of weak leadership.

You yourself mentioned that these trainings are mandatory. When you say mandatory I imagine "you either take the training or expect to be terminated due to failure to follow company policies". Probably this manager is taking this as a last resort reminder to the people not following company policies and requirements, and due to the mandatory nature of the trainings they are making a favor to these people to avoid them getting into trouble.

Staying silent and just "letting them face the consequences" would definitely be a sign of bad leadership and probably getting into immoral territory. Staying silent or continue doing the ineffective approaches they have done so far can also represent problems for this manager, and sending an email helps them to have a "paper trail" in case things go South and they has to give accountability to his higher ups.

You mention "shame" and "humiliation", but they are not doing it with that purpose. It's a "scream" for help, and to catch the attention of these people, and to have a paper trail as mentioned before... what's more, these people probably aren't ashamed nor humiliated by this lol, given that they are not complying with the training...

But does it actually violate any labor or privacy policies or laws? I plan to take my concerns to HR, but want to be prepared with any information that can bolster my objections.

Unlikely but I am not a lawyer nor your HR (your HR probably knows better and this manager very likely already ran the email-sending with them before).

Unlikely, also because you mention this is not done in a @everyone tag; it's done only in subsets of teams, so the email only reaches the ones involved or on a 0-degree of separation with the ones not complying with the training.

It's also likely your company already has a @team1 and similar mailing list configured on your email, making it easier to send broadcasts to the team, rather than they having to check one by one who is not complying and who is complying.

I plan to take my concerns to HR, but want to be prepared with any information that can bolster my objections.

If you value your job, do not take this concern to HR!

You have nothing to gain from doing that and you'd just be placing a target on your back for zero gain whatsoever.

Besides, there is no shaming or humiliation going on here either. Has anybody complained to you about it? I seriously doubt that.

Also, if we follow your thoughts to their natural conclusion, that means that you'd probably have a problem with management delegating tasks publicly and keeping track of those tasks during a daily standup meeting.

Again, if you value your job (and your reputation), do not voice this concern. Your social capital is very limited. Be careful not to squander any of it on pointless office battles. Pick your battles much more carefully.

But does it actually violate any labor or privacy policies or laws?

No, it does not.

I plan to take my concerns to HR, but want to be prepared with any information that can bolster my objections.

Trying to be the hero here is a mistake.

You might not like the management style here (I don't), but HR isn't going to change it because of your complaint. These trainings are mandatory for a reason and likely HR is at the core of that reason.

Instead, encourage your fellow workers to get their mandatory trainings done. That way, there is no problem.

If you feel this compelled, have a one-on-one conversation with the manager, and politely explain why you feel this isn't the right way to handle the situation. Suggest an alternative way to get the workers to complete the trainings that they are required to do.

Managers can yell at you in public

In the US, managers can yell at you about anything they want whenever they want. There are zero laws around this, unless they cross defamation laws (for which truth is an aboslute defense in the US) or do so against a protected class of employee. Certainly there are no laws making company training recods private.

You might not agree with their tactic (my opinion is whatever, it's just en email), but anyone feeling shamed or humilated becasue they haven't yet completed training that isn't even due yet has their own problems with life in the workplace. This is so mild that my immediate reaction is that you need to get out more. That said, yelling at employees to induce shame and humilation is not agaisnt the law in the US.

I can not really understand you, the boss could fire you at will in the USA. Why does he use such threats?

He could just call you in his office, and say you, that is your work duty, because the company/bosses above him want it. Then he would ask you, when will you be done.

After you are not done again, then he could say, you can choose between

1. Leave now or
2. Be suspended until you are not done.

In Germany, I could not be fired so easily (would require 3 written warnings, if I still not do, they could fire me for my bad behavior). As I have got such crap training materials, I absolved them on the spot. Why?

Because I wanted that the HR remembers me as someone without any significant problems.

Although I hate my employer and my work, because 10 out of 10 of their decisions are hostile, stupid or both, and likely I will resign soon, until that I work on a minimal acceptable level.

Why did I still absolve all the trainings on the spot?

Because I still did not want to extend the "area of conflict" on such a nuance.