When a QUALITY loaded bike is shimmying, it is most likely due to weight distribution. Assuming all the racks are quality, the racks are fastened on securely, etc. the amount of weight and where it is located is factor. Historically, you should have at least 40% of the weight over the front wheel, not the rear wheel, and all gear should be loaded as close to the the center of gravity and as equally balanced side to side as reasonably possible. This is also true for non-quality bikes but if a really cheap bike, the frame design & manufacturing itself may contribute.

If you have heavy rear panniers and all your other stuff loaded on the rear rack and a small handlebar bag up front, you have a decent chance to get shimmy, especially on a fast downhill.

Solution, put more stuff in front low-riding panniers. If my gear for a given tour weighs more than 25 pounds total, I will divide between front and rear panniers. I always put the heavy stuff (tool kit, batteries, food, etc.) up front. I personally strive for at least 50% up front as I really do not like to be going 30mph down a hill and start to get shimmy as I did in my early touring days. The only downside is it makes the steering much slower but unless you are doing bikepacking (which uses a different packing system typically), this is not a big deal.

If you want to test this, put a bunch of 1 gallon or 1/2 gallon jugs of water in your rear panniers only and a gallon or more in your handlebar bag nut nothing in front panniers, strap on a few pieces of firewood or something heavy to the top of the rear rack and ride down a steep downhill. USE CAUTION and don't blame me if you crash because you didn't slow at the first sign of shimmy. Then ride down the same hill after putting at least half the the WEIGHT in front panniers/rack and remove the firewood (weight transferred to front) to lower center of gravity. Again, keep the total weight the same, just distributed with at least 40% in the front panniers & rack. Any difference? This is because the weight is better distributed.

Another way to look at this is it is similar when pulling a trailer in a car. If you put the too much weight toward the rear of the trailer, the trailer starts to shimmy causing the car to shimmy (tail wagging the dog). That is why you are supposed to have about 10%-15% of the weight on the tongue (coupler) of the trailer for safe trailering.

Tailwinds, John