Do you find that pointing out inconsistency actually changes people's opinions much? Usually it just puts them on the defensive. It might be worth it for the benefit of third parties I suppose.

Actually changing people's opinions once they're formed and emotionally vested is really hard.

It works on rational people. These are unfortunately rare, and not trivial to identify before wasting effort on a discussion which can only lead to pointless flamewars.

It would help if the strength of someone's opinion was proportional to something meaningful, like supporting evidence, or how much they'd thought it through. Then "the defensive" might actually be a sound counter-argument. Bingo, useful discussion.