1969 Dodge Dart 4 door - Folding bench seat?

How much less stable?
I don't know, the only time I have seen it done is for a racecar when they are adding a roll cage. Don't forget that these cars are unibody's, so every structural member is there for a reason to keep the body stiff. If it is just a driver with not much extra horsepower then I think it would be OK, I was a design engineer in my working life...