Do not use pressure / power washers.
Do not use bleach or salt-laden cleaners.
Do not use wire brushes or other coarse brushes.
Do not sand blast or use power tools.
Get permission from the cemetery owner.
Perform small test patches before cleaning.
Use the gentlest cleaning method possible.
Have patience.
NCPTT Cemetery Preservation Course https://www.nps.gov/articles/000/cemetery-preservation-course.htm
Veteran's Administration Cleaning Guidelines https://www.cem.va.gov/hmm/cleaning.asp
Gravestone Conservation Website https://gravestoneconservation.com/
Association for Gravestone Studies Website https://www.gravestonestudies.org/
Cemetery Preservation Subreddit https://old.reddit.com/r/CemeteryPreservation/
Chicora Foundation Website https://www.chicora.org/cemetery-preservation.html