Weird noise after shocks/struts replacement

Are the sway bar end links purple? That usually indicates they are not rubber but stiffer urethane, which also loves to squeak. You could test that by removing the end link. From that side and see if the noise goes away. If it does you can try applying some silicone grease (like sil-glide) and see if it stops.

That stabilizer bushing on the frame should be replaced as well but those usually will make a clunk if they are completely bad as the bar will hit the mount around it.

Not bad as in failed, more like the wrong application of a material. Factory rubber bushings are sort of like marshmallows. They can flex and move a lot because they are soft. Urethane is stiffer normally which can improve handling but it also has a bad property of squeaking sometimes. The easiest test is to simply remove the link and see if the squeak goes away. If it does you can apply either silicone grease (will not damage the urethane) or get factory type rubber bushings.

As long as you do not race it or try to corner like an F1 car it is not a problem. Plus you should be able to tell rather quickly if the noise is gone. Also, you mentioned in a different question that the car leans/pulls to one side. It is very possible that alone is putting stress on the suspension and causing the squeaks because of that alone.

Overall I would try to get that fixed first. Then see if you still have the noise.

Okay, got confused with the vehicle. As far as racing, you might be surprised at what some folks try in a base vehicle.

Just checking to see if you have made any progress?