I just wanted to throw one more voice into the mix. I am the pre-team program director at our gym. We look for a mix of skills, strength, flexibility, and dedication/drive/love/focus/ability to make changes.
For our youngest pre-team (ages 4-6), we look for kids who have unusually high levels of coordination and focus. They can do a pullover off a block, a forward roll on the floor, a backward roll down a cheese, cast on bars, as well as a passable cartwheel and handstand. Most 4 and 5 year olds can't do these things, but this pre-team group is to keep those who can moving forward, rather than being bored in our 4-year old and kinder classes.
For our next pre-team group (ages 5-7/8), we start to look for a balance of skills, strength, flexibility, and focus. They need to be able to do 2-3 pull-ups and 2-3 leg lifts, a split within a couple of inches of the ground, and a bridge with straight arms. They can do a cartwheel and handstand, a forward roll and backward roll; a pullover, cast, and back hip circle on bars; run and hurdle onto a springboard; and are comfortable walking, jumping, and turning on a high beam.
With gymnasts older than 7 or 8, I look for them to have the skills to compete JO2 (or occasionally, go straight to JO3). That means to go into the JO2 group, they need to be able to do all their JO2 skills (exceptions being I'll take a kid who doesn't quite have her mill circle and/or her bar dismount), 5 pull-ups and leg-lifts, as well as a split all the way down, and a bridge with straight arms and legs. For JO3, they need all the skills again (occasionally I will take someone who has their RO BHS on TumbleTrak but not quite comfortable with it on floor), 10 pull-ups and leg-lifts, two splits all the way done, and a bridge with shoulders over hands. These standards are shared with any parents who ask and shared with girls in our intermediate and advanced rec classes, so the kids know the standards. It's quite common that when girls come to pre-team evals the first time, they aren't "ready," but I email their parents with what they need to work on, and at the next evals 3-4 months later, they are usually ready.
Anyways, this is way too much detail, but I thought it might be helpful to see how standards and expectations vary gym to gym and by age and level.