The harley factory shields have a coating.
An abrasive will alter/destroy the coating.
When the coating is destroyed it will cause the area destroyed to become visible with polarized sunglasses.
Leave it alone or replace.
Although some cleaners can make it a little less visible if it is left alone.

 

For minor scratches and abrasions, I've used Maguiar's PlastX (clear plastic cleaner and polish) with good results using a low speed buffer as well as by hand. Any scratches beyond minor, you should probably replace the shield, especially if they impair your view.

Someone mentioned toothpaste, and to that I would say no, don't do it! I did that once and learned my lesson the hard way many years ago. It may look fine in the shade, but in the sun you will have no visibility whatsoever through the area you used the toothpaste on.

 

Absolutely. I wrecked the windshield on my Low Rider by trying to buff out a scratch. I kept going and going, and
eventually the scratch was gone, along with the outer coating in the area I buffed. It looked absolutely terrible, visible
from a mile away.

I ended up getting a new windshield.

 

If it's small scratches/swirls I've had better luck using lemon pledge or a spray wax to fill in the scratch. Almost everything I've used to buff/eliminate scratches just made the shield look much worse in the sun or oncoming lights. jmo

 

I got one of these from the maker at their shop. They are an upstanding company. Windshields aren't all they make kind of a sideline. They custom mold plastics for mainly vehicles for companies that need special interiors. They gave me a tour of their plant. I have one of their shields to replace my stock Harley shield which had a lot of buffeting no matter what I tried including fangs. This was on a detachable on a Softail Slim. With the LRS there is no buffeting whatsoever. They are not expensive, go that way.
kk

 

I've had good luck using a product named Flitz. I took out a fairly deep scratch on my Ultra Limited screen and you couldn't tell it was ever there.
Amazon has it.
Bill