"In principle" means fundamentally. "On principle" means according to personal manner of behaviour. Only one person can go on strike "on principle" because other people might have different manner of behaviour. So, in order for many people to go on strike, they need to oppose to something that is fundamental to all them, not just one person.
For me it's the opposite; if you oppose something 'on principle', it's fundamental, but 'in principle' is a starting point that can be negotiated.