If its just for the track no doors would be fine.
On the street may be another issue. Are your passangers going to want to step over ??? Think about the lady in your life
I doubt she'll be too happy about it in a skirt on a dinner date.
The other street issue that comes to mind are saftey laws. I would check your states inspection laws.
Just my 2 cents.
The great thing about these cars is, ITS YOUR CAR. do it up your way and enjoy it.
Harvey R