it seems like we see an inversion of obedience today, with people promoting obedience to sin and disobedience to virtuous pursuits

Obedience is often considered to be a virtue and that shouldn't be forgotten; yet naturally in the Scripture there is the the example of the king who ordered the worship of false idols, who was disobeyed (book of Daniel). This is still considered to be obedience to God though, rather than men (Acts 5:29).

Generally unjust laws have been tolerated, unless a person is being compelled to sin, like in the above example of false worship.

Naturally also an informed conscience might make conscientious decisions in uncertain situations, where it does not seem clear what the right thing would be to do (conflicts of law or commands versus morality?).

Christ was obedient to unjust sentencing by political authorities, even unto death; hence even this kind of obedience may be thought to be good at times:

He humbled himself, becoming obedient unto death, even to the death of the cross. Phillipians 2:8