Farmers protests across Europe: are the farmers right?

Farming in Europe is, for the most part, not viable. It is a loss-making industry that is totally dependent on large state subsidies and artificially high prices. The reason those subsidies continue to exist is largely because governments see maintaining an agricultural base as a form of food security - if we rely on somewhere else for all our food, we're more vulnerable to disruptions - what if there's a war or natural disaster there that severely hits their farming? Or even in more mundane terms, it would severely increase their governments' trade negotiating leverage with us if we didn't have at least some agriculture of our own to fall back on. Is that a worthwhile trade-off? Eh, your mileage may vary.
Additionally, when you think of "farmers", you might have an image in your mind of a few fields around a quaint little countryside family house, where the main farmer is the family patriarch and the work is all done by him with help from his wife and kids, and where they have a handful of farm animals who've all been given names, etc. Those places exist, for sure, but they're declining and are not really the backbone of European food production, in fact their farming is likely even less viable than the industry as a whole. They're getting income from selling their limited produce through farm shops, local markets, and other niche outlets where people will pay a premium for local small brands, from renting out spare land or buildings for things like storage, camping, activities, etc, and other stuff that you don't really think of as "farming", per se. The somewhat more viable (though still hugely loss-making without subsidies) farms are much more likely to be large, industrial, mechanised, sprawling areas that employ at least tens if not hundreds of workers, owned by sizable private businesses which might well have a more bureaucratic ownership structure, with partners, shareholders, etc.
This is all a pretty long way of saying that if we're going to continue to provide such subsidies, it's pretty reasonable to insist that the farms transition to more ecologically friendly methods as part of the deal. So no, I don't really think their protests have much merit.