You can stabilize the part and stop the wobbles by manually painting supports on the vertical surfaces. As the nozzle moves around on a layer, the filament drags on the model and drags it out of position. The supports will resist this movement but do not actually touch the part.
In the case of this model, I’d paint the rods at a height where the print is still stable. About halfway up the short rods, but the tall rod will probably need supports at about 1/3 and 2/3 height.
You may want to experiment with support brush size. I usually paint just a small dot, but on both sides of the part. Sometimes a large dot just on one side will wrap further around the part and provide enough stabilization.
I usually reduce Support X-Y distance to 0.1mm to minimize movement. Try slicing with different Tree types, but Organic usually uses the least filament.
