So if there is a secession movement, it should always be supported?

Your thought process is very unique haha. Not sure how you connected those dots together, but it seems like you spotted the issue with it.

What of the people of Hong Kong who supported further integration into the mainland? Do they not matter?

So different people who make up a single state have different policy positions? Hmm.. how might we resolve that conflict?

One solution that's been commonly used is democracy.

Instead of forcing people to "always support succession" for some unknown reason or to have your state always supress succession (like Putin does), we could strive for a middle balance where people are free to speak and support whichever secession movements they want, form parties, and these issues are then put to vote.

Think how Brexit, as dumb as it was, wasn't a civil war. It was just a referendum.

No one has to die changing the government.

How about the neonazis trying to turn the Pacific Northwest of America into their "Northwest Territorial Imperative". Should we support those secessionists?

In a democratic sense you should support the secession movements you agree with and not support the ones you don't agree with.

So why are you asking me? Ask yourself if you support turning the Pacific Northwest into a Northwest Territorial Imperative?