First, I played football, basketball and baseball in high school. I also skied on my own. I grew up in an era of play the sport in season. When the kids were little (daughter five years older than son) they were introduced to as many team and individual sports as possible based on the season.
By high school my daughter (played college softball) played volleyball, basketball, ran second team 200m and 400m relays on Saturday nights for indoor track without practicing and softball. Because there tend to less number ot athletic girls they were encouraged to play multiple sports. Even a girl who made Team USA at sixteen and js now considered the greatest American in her sport played a second sport.
My son had played travel soccer since he was eight. When he got to middle school he switched to football. He also played basketball and baseball. Heading into high school he decided he didn't want to risk football injury and missing any basketball or baseball. He returned to soccer. As a whole the boys coaches didn't like varsity athletes playing a second sport. It was a large classification, very athletically competitive high school. My son was playing three sports.
The soccer coach was very unhappy with my son playing other sports and not playing for an elite summer soccer program. He appeased the coach by attending an elite summer goalie camp on weekdays.
My son was the starting point guard on the JV basketball team freshman year. There was a lot of speculation he would start varsity soph year. He was the ideal point guard. He was in search of the perfect pass on a team full of gunners.
I came hope from work one evening to find my son slumped on the coach. He was cut from the basketball program. Not even returned to JV, cut. By happenstance later that night I ran into the coach that night at the grocery store. He explained he cut my son because he was on varsity soccer freshman year, expected to start at short in basebal soph spring and never showed up for one optional basketball workout all year. In the years my kids were at the high school only two basketball players played two sports. Both were 6'7". One went on to play for Man U and in the MLS. The others tonight to be an NFL edge rusher.
My son continued playing basketball in our town's very strong youth basketball program. Jv, freshman and varsity bench players not getting minutes were allowed to play. An all star team probably could have competed as a 3A (of 6A) high school team. A former NBA player/dad would siting the stands at the high school games screaming at the basketball coach his best point guard was sitting in the stands. My son eventually thanked him and politely asked him to stop.
Not playing school basketball allowed for two positives things. 1) It allowed time to workout and bulk up. 2) He stopped running of a bunch of weight in basketball practice. The baseball coach had been a two sport high school athlete. His attitude was play any sport you want. But you better show up day one in mid-season form. Freshman year my son was at baseball training at 5:45am because he had basketball practice in the afternoon.
Back to football ... My son stopped playing football after middle school out of fear of getting hurt for other sports. He tore his MCL and PCL the first weekend of post junior year playing travel baseball. He spent months on crutches. All the hot onhis trail college basebal programs disappeared (it all worked out). Then he fell and separated his shoulder, requiring surgery doing rehab on his knee. Before getting injured the football coach saw him punt a soccer ball and recruited him to punt for the football team.
To net it all out it's a matter of balancing the situation. Do what you love. Play hard. Don't think about getting injured. If you fear injury, don't play.
Add note: College coaches say they like multi sport athletes. The reality is they like the best baseball players even more regardless of multi sport or not.