I feel like it's much easier to sympathise with the supporters of one king against another (plausibly genuinely worse) king than in a king vs. republican conflict.

I feel the same way! The Royalists/Chouans/Vendée soldiers might also have that loyalty and honour vibe, but it feels harder to find them relatable, so the fact that we can, even in a small way, probably speaks volumes about Broster's talent for writing!

I can see myself getting into so many new historical periods and settings because of this

That's one of my favourite things about reading! :)