Normal with vehicles with bad or insufficient shock absorbers. I nicknamed the effect "Hobby Horsing". Despite their horrendous cost I started using KONI shock absorbers along with the largest sway bars I could fit front & rear. As I have aged my driving skills have deteriorated markedly. Improvements in control and handling to me are borne of necessity to keep out of accidents and stay alive. The Koni shocks I fitted to the toad have gone eighty-thousand miles without needing to be adjusted stiffer setting. I have this peculiar fettish about safety being worth the money. One tiny accident would cost more than ten sets of Konis and sway bars.
The toad has independent rear suspension. The rear sway bar has done ZERO to degrade the handling of the car hitting deep Mexican grade one wheel potholes. With a solid axle and leaf spring rear end the non-effect of torsional flex applied to the other side is even less if that means anything. 50-years ago when I was auto-crossing in the Tiger sway bars became detrimental in a G-force 180 when it would lift the opposite side tire off the ground. If I tried a stunt like that in the toad I would slide off the road in a skid. The sticky 4.50 10
50 13" Goodyear Blue Streaks created the sway bar tire lift phenomenon.