A nation can change, a people can become corrupt, the values stay and if for example a democracy steered by corrupted peoples betrays itself, a democrat with values can just soldier on without getting into any loyalty conflict. A sadness for what has fallen may linger.

A nation? Or a economic zone?

A people? Or a population of foreign guest workers?

Not really. Have you ever heard a saying, "right or wrong, my country"? That's exactly the kind of toxic stuff that loyalty to entities leads to.

Your use of language is imprecise. What exactly is meant by "my country" here?

We have the state; we have the ruling regime; we have the society in question. Who is this "country" that is right or wrong exactly?

If the state, then in the abstract, it is authority without particular directive. So it can't be that.

If the ruling regime, then it can undermine its own authority by demanding people commit evil deeds. But it is not betrayal to refuse to commit the evil deeds it demands. It is the ruling regime who betrays the society it rules by demanding evil. Remember: lex iniusta non est lex.

If society, then we're talking about an aggregate and therefore mob "rule". But who cares what the mob thinks? The mob has no authority.

Betrayal and loyalty can only be measured in relation to the objective good. I agree with you that "my country, right or wrong" might suggest something very evil, but to reject the suggested relativistic understanding of loyalty is not betrayal. You could interpret it differently: I am loyal to the good of my country, regardless of whether my country is in the right or in the wrong. And the good of my country might involve opposing an evil regime or standing up to the mob. That's true loyalty. Obedience to evil is false obedience and true betrayal.