Athletes are permitted to cross to two additional teams beyond their "home" team. It is allowed per the rules, but whether it is looked down upon or not in people's personal opinion varies a lot by how a gym uses crossovers. There is currently no industry wide restriction on what skill levels an athlete can cross between, but some competitions do put restrictions on it. I believe NCA Nationals only allows a certain number of crossovers per team/program, and they all must cross between the same level (level 1 to level 1, level 5R to level 5, etc).
Some programs put a vast majority of their athletes on 2-3 teams. Sometimes teams are made up almost entirely of crossovers from other teams. There are kids that really enjoy the challenge of being on multiple teams and learning different skills and routines and gyms allow them to cross. It can be considered a great learning opportunity for some athletes, because while a child may be a great Level 3 tumbler, they may really want to fly, but not be anywhere near having level 3 skills. So, they will get placed on a different, lower level team, where they can learn flying skills. Some gyms use crossovers to fill open spots on teams.
Other gyms rarely, if ever, use crossovers, sometimes only in cases of emergencies (injuries, illness, kids quitting last minute).