I understand why Caledonians don’t like the bill, but to answer your questions: yes, they can vote for the French Government, as they are by law French Citizen (as well as Caledonian Citizen, in opposition to someone living in Marseille which only gets the French citizenship and no Provençal citizenship, for instance) They also have a higher autonomy than other French region or department (imo it’s a good thing as they definitely have quite a different situation than metropolitan France regions)
I understand that this situation can look colonial-ish to outsiders, but according to the last referendum, a big majority of Caledonian people wishes to stay French. And they are full French citizens. This is a protest like those in Paris, against our (shitty?) gouvernement, not a protest for independence, afaik