Is shingles contagious through handling the laundry of someone with open sores?

No.

Shingles is caused by the varicella-zoster virus, which is the same virus that causes chickenpox. People who have shingles can spread the virus to people who have not had chickenpox or the chickenpox vaccine. However, the virus is spread through direct contact with the open sores of someone with shingles.

You cannot get shingles from contact with someone else's laundry. The virus is not transmitted through clothing or other objects.