I wrote to the CIF and received this response:
"There are no relevant C.I.F. Southern Section rules regarding a player playing Varsity and/or J.V. during a particular season, that is an issue for the school's coaching staff.
The only rule we have regarding this issue is a rule that states a player cannot play two levels of the same sport on the same day. So, a player can't play in a Varsity baseball game and a J.V. Baseball game on the same day."