It comes down to the simple reality that "I am because we are" and as such any time a human being is oppressed we are all oppressed.
One could make the argument the people who live in liberal democracies have an obligation to help those who unfortunately do not and who are still forced to live under autocratic oppression.
There were periods in history where most people lived under the thumb of some sort of autocrat of one form or another be they monarchs or religious leaders. Most people had very few human rights and had little opportunity for self-determination. Through the hard work of revolutionaries around the world many of those autocrats were deposed and others seeing the writing on the wall offered power to the people more willingly.
Think of it like a jailbreak where the jailer is oppressive and everyone in the jail is innocent. On your wait out should help open the cells of as many people as you can if only out of your own self interest because a larger mob escaping gives each individual a better chance to escape due to strength in numbers but also because it's just the right thing to do.
It's sort of the same thing here, Our ancestors (or even some of us) got out from under the thumb of an autocrat jailer but there are still others in that jail. If we don't help them who will? What would you want someone else to do if you were in their situation? To walk by an unjustly imprisoned person's jail cell and not free them when it is trivial to do so makes you the jailer.
Now that's the theory. In practice, I agree with much of what you're saying -- reality is a far trickier place than we'd like and the details make doing the right thing difficult if not impossible. And that doesn't cover the reality that western democracies are imperfect themselves and that many of their citizens are still subject to repression by their own autocratic leaning leaders, and so that we can't always do the right thing, but we should at least aspire to.