Tough question to nail it down completely but from prior experience I can at least point out what needs to be done at different levels.
1) If building the car to a specific class can make a difference in how much weight the car must maintain and what parts must remain like dash, even front door panels, etc....and how much cage it would require.
2) If building to what you want to do and then just running whatever class you had to then you can do pretty much as much gutting as you wish. There is a lot more weight than just the full interior which is quite a bit to remove, sound deadening, a ton of excess wiring, some lessor mods but it does add up like unneeded brackets, longer than needed bolts and studs. Also air bags which are pretty heavy, my car has a sunroof so that can be quite substantial, also air conditioning, heater core, etc....if get really into it lexan windows in the rear, window acutators, trunk latch, even door latches. One can build a minimal legal cage and end up much lighter than my car is now.
3) Tying in the cage to the strut towers, rear suspension pickup points, stronger door area, some can be done with smaller tubing. Also it would be easy to be under 2500lbs so .095 DOM
in 1.75" would be plenty strong and lower in weight though 1.5" might meet the requirements. I have a nice tubing bender, notcher and dimple dies I will be selling soon
I built a Scion TC, caged with some removeable elements, CF/Kevlar roof, 18x9" wheels, foam filled chassis, two race seats and harnesses, nearly full interior kept, sound deadened, boosted, wing, splitter, etc....and it was 275lbs lighter than stock. It did not start out much heavier than the FiST when I bought it new.
There is a thread on the forum about a race build that might shed more light on how low the car can go down to in weight but I imagine 2300 lbs may be doable.