There are coaches who feel thumbs should stay next to the forefinger on almost every skill except handstand turns, and of course coaches who feel they come in handy in specific positions....... but can't remember any who felt thumbs could remain wrapped around the bar during circling skills like clear hips, toe hands, stalders, and giants.
You can get an idea of where, during a bar routine, thumbs may help provide a stable base for the support phase of bar skills like casting from the bar, and handstand moments by watching Gabby Douglas on bars. My use of her as an example isn't an argument of "thumbs up" on thumbs, but because she's a convenient example where you can clearly see her thumbs moving from a unified hook to an opposed hook position.
The reason I may tell a kid to use her thumbs is that most girls have to flex and sag through their wrists to center their hands over the bar during support phases. The backward flex makes it harder to maintain straight arms and the correct body shape for some gymnasts moving through these positions/skills, and using thumbs helps them keep their wrists in a a more comfortable and powerful posture.
So if you have two differing attitudes coming from the coaches at your gym, and are allowed to choose the style that works for you....... Try whichever thumb method you're not using now for a week, as long as you're done competing for the season, and see if the new method equals your original method. If it shows promise, pursue it for another week, then evaluate it again and decide what to do.
Oh yeah.... Please make sure both/all of your coaches know what you're doing so you don't end up with a coach apocalypse on your hands.
