Inflicting damage is usually justified by averting larger damage. Very roughly, breaking a $200 car window is justified in order to save a $100k house from burning down. Stealing someone's car is justified when you need a car to urgently drive someone bleeding to a hospital to save their life (and then you don't claim the car is yours, of course).
I don't think Luddites had an easy justification like this.
One one side there were the luddites and their livelihoods; tens of thousands of people.
On the other side, there were cheap textiles for EVERYONE - plus some profits for the manufacturers.
They might have been fighting to save their livelihoods, but their self-interest put them up against the entire world, not just their employers.
It’s an interesting question because the benefits of automation aren’t necessarily shared early on. If you can profitably sell a shirt for 10$ while everyone else needs to sell for 20$ there’s no reason to actually charge 10$ you might as well charge 19.95$ and sell just as many shirts for way more money.
So if society is actually saving 5c/shirt while “losing” 9$ in labor per shirt. On net society could be worse off excluding the one person who owns the factory and is way better off. Obviously eventually enough automation happens so the price actually falls meaningfully, but that transition isn’t instantaneous where decisions are made in the moment.
Further we currently subsidize farmers to a rather insane degree independent of any overall optimization for social benefit. Thus we can’t even really say optimization is the deciding factor here. Instead something else is going on, the story could have easily been framed as the factory owners doing something wrong by automating but progress is seen as a greater good than stability. And IMO that’s what actually decides the issue for most people.
In regards to both the Luddites and the farmers, you seem to forget the most important factor. Food.
In the case of the Luddites, it was a literal case of their children being threatened with starvation. "Livelihood" at the time was not fungible. The people affected could not just go apply at another industry. And there were no social services to help them eat during the transition period.
As for the farmers, any governing body realises that food security is national security. If too many people eschew farming for more lucrative fields, then the nation is at risk. Farming needs to appear as lucrative as medicine, law, and IT to encourage people to enter the field.
I'm pretty sure the Luddites judged the threat the machines posed to their livelihood to be a greater damage than their employer's loss of their machines. So for them, it was an easy justification. The idea that dollar value encapsulates the only correct way to value things in the world is a pretty scary viewpoint (as your reference to the value of saving a life illustrates).