[Steve Tinker]

Tex....
When I replaced my drop links & control arms earlier this year, I don't remember the sway bars being able to move laterally, but I think they will if the wheels are off the ground and the drop links & bushes are worn / loose. Certainly the drop links rattle when worn - you can replace them quite cheaply.
You can replace the sway bar bushes with aftermarket, I just removed them, cleaned the bushes and lubed with lithium grease as they were squeaking. They were tight on the bar.

The drop liks are a favorite wear item if your car has done a big mileage or driven on rough roads (do you have rough roads in TX?), but I think they are only about $50 each to replace. As a temporary cure to the rattle, you can remove the drop links, prise open the rubber boot from the shaft end and fill with lithium grease from a pressurised can - this will (should) stop the rattle temporarily.

As a side note - I chased a front end rattle for months - replacing first the drop links, then the steering rods, then the shock top mounts and finally the lower control arms. Of course it was the last item to change out at fault (control arms) but it cost me a lot of time, effort and money as you cant tell whats worn just by levering the suspension or bouncing the car while static......