Gymnasts who do not take care of their hands miss an awful lot of training. Male gymnasts have more support and hanging event work (PH, Pbars, Rings, and High Bar) so hand care can be a huge issue. Here is the advice I've always given to the guys I have coached:
1. Don't over do it - when your hands begin to feel like they are going to rip - they ARE! So say something!!! There are plenty of other things that can be worked on. Steadily/gradually the skin of the hands will toughen up and the amount of time on events will lengthen... AS LONG as you avoid the rip-heal-rip cycle.
2. Take care of your hands - avoid rips but also minimize the risk by maintaining good skin health:
A. When a callus builds up - especially when it forms a noticeable "ridge" - use a pumice stone to gently grind it down. A pumice stone works best on DRY skin. Don't use it right after washing your hands.
B. Keep your hands clean - wash them before and after workout with warm water and soap. It's especially important to wash your hands immediately after workout. Magnesium Carbonate effectively absorbs the oil in our skin... If you leave it on the hands for prolonged periods after practice the skin around your nails may crack/split and THAT can be very painful.
C. keep your hands moisturized between workouts - any skin lotion that contains "lanolin" (animal oil) is great.
Many Olympic caliber gymnasts put a lanolin-containing lotion on their hands at night and wear cut-off (no fingers) cotton gloves to bed to soften the thick calluses - especially those on the heels of the hands (from PH and Pbar work).