Boys were another story. A majority of the male coaches thought they owned their players. My son played three sports freshman year. Soph year he was cut from the basketball program for not playing in a summer basketball league and missing optional workouts all year. He was the only soccer player not playing summer travel. It irked the coach. My son attended summer goalie camps to appease him. The baseball coach was one of the few coaches who encouraged multiple sports. Seven players played two sports. But they were warned about attending winter workouts. There was a 5:45 am workout session twice a week for those playing winter sports.
100 pct opposite at my kids school. They have early am long toss sessions. We where specifically told that if a winter sport participant showed up he would be sent home. We'll find out the ramifications in about 30 days.
Our school is very adamant about winter sport athletes not attending the "open gym's" for the spring athletes. They don't want to take the chance of an in season athlete getting hurt getting ready for another sport.
In this day and age, I think that is a "silly" position. Many kids are working out with their club teams anyway. As far as baseball is concerned, I view off season throwing as relatively low risk of current sport injury, but very important in conditioning one's arm. Not throwing is the equivalent of me getting my fat a$$ off the couch to run a 5k -- I am not gong to make it very far.