Do I really need a sway bar

It might very well be a metallurgical fault. 20 years ago, a microscopic flaw destroyed an airliner and took 110 lives (UA 232).

I find it hard to believe that a Mustang with a relatively low center of gravity will tip over. However, it will cause the car to understeer more. You’re less likely to spin out on the road, but you’re more likely to run straight into what you’re trying to avoid in an emergency