Most commonly people still manage to fly on ticketed bookings with supposedly reverse name order. The check-in agent may have to pull up your record with the alphanumeric record locator and manual entry of the opposite name from what comes up in the passport swipe, but it generally works fine. The passport data can still be stored and transmitted however it should even when then ticketed name order is supposedly reversed.

Lots of people with roots in various parts of Asia and Africa have traditions of family name being the first name and then personal name being the last name. While some agents may make an issue of it and ask someone else what to do, I've seen lots of people fly in such situations without problems beyond the check-in mini-delay.

This isn't a guarantee that the past will repeat itself as it most commonly has, but even now it's generally not a trip stopper.