I SOO hear where you are coming from. how old are you? I just finished my second year of FIS, and pretty much picked up newschool seriously this winter. Hopefully I can give you some insigt to your decisions.
I've thought long and hard about what to do with my skiing career. When racing, I'd watch videos and often feel I'm falling behind where newschool is going. I just keep doing it as much as possible. I see the value of racing, and I actually *gasp* enjoy it (ill get flamed for this one). But, I probably enjoy newschool more. Why do I keep racing? well, it gives me the opportunity to ski every morning in the winter. If i get on top of my school, or if i feel like it I'll skip and ski park in the afternoons. Plus, it gives me the opportunity to go on all kinds of training camps to far away places where you can ski off season when most newschoolers are in, well, school. Also, The feel that I've gotten from racing has helped me learn newschool much faster. Every time I go out I can learn something new.
What your father is saying about 'supporting' newschool and stuff is similar with my dad, he is ok with me doing it, so long as it doesn't conflict with my racing. I understand this also, because he's the one who is paying for it.
The compromise that I make, is that I get to go to whister in the summer and ski newschool. Sure I get less days of newschool, but I make sure I work on some sort of newschool everytime i'm at the mountain. even if its just a little bit. whether its skiing switch, taking off switch off little jumps--all of which can be done in your race skis, or even bringing your twintips to the hill to ski the park while the coaches set the course. every little bit counts.
Keep pushing and ski AS MUCH AS POSSIBLE. if quitting racing means that you ski less, you'll probably be a better jibber sticking with racing.
Another option you may want to look into if your parents have the funds, is going to a ski academy.
The structure of an academy oriented towards newschool (like CVA for example) could prove to your parents that you are a dedicated athlete with regards to jibbing. you'll do dryland training, trampoline work and all of that cool stuff and become a pretty sick skier in the process.
Basically, my word to you is to not shut any doors. if you can ski lots, and do both, just remember you get many more ski days than most people. I know it sounds funny, but someday you might regret having quit racing.
thats my 2 cents (maybe stretching on to 3 cents)
Life sucks, get a fucking helmet