If you're feeling nice, randomize whose time remains stable (to keep things fair), keep the organizer's time stable, or pick the time that minimizes the number of participants who will have the meeting time change.

If you're feeling mean, randomize whose time remains stable (to make it hard to predict), move the meeting for the organizer, pick the time that maximizes the number of participants who will have the meeting time change, or split the difference and move everyone. Meeting was at 10 AM for Alice and 9 AM for Bob, but now it can be at either 11 AM for Alice and 9 AM for Bob or 10 AM for Alice and 8 AM for Bob? Now the meeting is at 10:30 AM for Alice and 8:30 AM for Bob.