Looks like maybe the wrong type of product was used. Something glossy or silicon-based.
Whatever it is, you need to get rid of it before applying anything else. I would recommend using a good quality all-purpose cleaner (Koch Chemie Green Star is my fave) diluted down with water to about 1:10 in a spray bottle. Use it in conjunction with a soft-bristle detailing brush to agitate the surface. Then wipe clean with a damp microfibre cloth.
Assuming it's not been permanently damaged, that should restore things to a nice clean and matt finish.
You could then call it a day at this point, or add a water-based dressing that claims to offer UV protection, and anti-static properties.