My tan colored vinyl siding is fading along with burgandy shutters,

Ask the manufacturer or a Paint Company (Customer Service) what they might suggest you use. Had a thought, Maybe something that refreshes the colour of cars etc. might be of use.........

I had blue/grey siding that was 22 years old. I did replace the as there was damage in a few places. I painted my burgundy shutters and put them back up. They turned out great. Would have made the faded siding look better with the brighter shutters. A paint store would be able to help you with the type of paint you should use.

Hello Ellen ! Vinyl siding can definitely be painted, as well as shutters. You can do them yourself or look online in your area for folks whose job it is to do that type of work. Click on the link below to view information specifically about painting vinyl siding. There is some good advice there. Good luck.

https://www.bobvila.com/articles/how-to-paint-vinyl-siding/

I would definitely paint the shutters, but check with your siding to see if there is a warranty before painting them.

If it was me I would paint it to freshen up the color.