I'm not going to encourage you to do one thing or the other here. I'm just going to lay out the legal hazards as best I can (I'm not a lawyer or a JAG) so you can make a more informed decision.

The potential legal hazards (i.e. NDA offenses) you're exposing yourself to if you engage in various forms of individual or collective disobedience relating to an order to intervene against the protest (from most severe to least severe):

• Sedition (life sentence)
• Mutiny (life sentence)
• Insubordination (life sentence)
• Desertion (5 years)
• Connivance at desertion (2 years)
• AWOL (2 years)
• Conduct to the Prejudice of Good Order and Discipline (dismissal)

Depending on what you actually do (or don't do), you could find yourself higher or lower on that list.

For example:

• If you just don't show up to the operation at all, you'll be committing AWOL and possibly desertion (and if desertion applies, any service member who knew you were going to desert and did nothing will be guilty of connivance at desertion).

• If you show up but then say "No, I'm not going" when ordered to deploy and instead just sit on your rucksack and refuse to budge, you'll be committing insubordination.

• If you and your comrades collectively disobey and also make demands of the government or the chain of command (i.e. "end the mandates" or "cancel this operation") then you're committing mutiny (because you're wrestling command away from lawful authority).

• If you say "Let's bring this government down by force!" then you're guilty of sedition.

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As you've been taught, you have a duty to disobey an unlawful command. But understand that the government ordering you to go in and break up a protest probably isn't unlawful. The law permits you to be deployed to do such things (this isn't the US where there are laws against federal soldiers being deployed against their own citizens). No emergencies act invocation is required. The Aid to the Civil Power clause of the NDA (sect 6) permits this. So being told to deploy against the protestors isn't in itself an unlawful command.

However, if an individual order at a lower level is unlawful (for example, being told to open fire on a crowd of unarmed civilians) then you're legally obliged to disobey that order. If you carry that order out, you will be legally liable for it (Nuremburg principle IV).
"I was just following orders" will not be a defense.

Whatever order you decide to disobey on legal grounds, you make damn sure it's actually an unlawful command and that you can prove it in a court martial.

Disobeying a lawful command on moral/ethical grounds however is a personal choice you have to make on your own.

So if you feel morally compelled to disobey an order to deploy against the protestors, then you do you. But don't commit mutiny by making demands of the government or your chain of command and don't commit sedition by calling for an overthrow of the government.

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Edit:

Also understand what conscientious objection is. It's basically just grounds for a voluntary release based on religious/conscientious objection to your duties. I don't think it would be much of a defense in an insubordination trial, but again I'm not a lawyer.