I never quit my bowling leagues as my seven kids were growing up. My kids all bowled on Saturday mornings so there was no conflict there. I didn't bowl weekend tournaments while they were in youth leagues, but that was okay with me.
When it came to other sports, my wife and I asked them one question, "Are you playing for yourself or are you playing because you want us to watch you play?"
If they are playing for themselves, then they don't care if you miss the occasional game due to league night. If they are playing for you to watch them, then they shouldn't be playing.
In short, you can do both if you really want to. Real conflicts can be handled with a sub for that week.