What Will said.... Manual Trans Fieros are great for that because of the offset dog bone mount. Automatics can do it to a lesser extent. My auto did it under sudden load changes. They will often even show wheel alignment etc are all good. The uneven load makes the cradle twist in the car. I drove one stick car awhile back that was all over the road when you shifted. It had just had a bunch of work done but they didn't replace the cradle set.
15-20 year old bushings just aint gonna do there. Installing polyurethane or solid metal cradle bushings will stop allot of problems, including most or even all this one. No, you don't have to worry about polly squalking here... There won't ever be enough movement to cause that.
You could need other work but I would start there with all the 84-87 cars.
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The only thing George Orwell got wrong was the year.
The Ogre's Fiero Cave (It's also at the top of every forum page...)