It is always best to preserve any food at its peak ripeness and freshness. Tomatoes that are overripe can be a problem if canned.
The acidity level in tomatoes varies during the growing season. If overripe, they are less acidic than when at the peak of ripeness.
Do not use damaged tomatoes or any that have mold growth. These may contain harmful pathogens that may not be destroyed during the canning process.
The best preservation method for these tomatoes is to freeze them.
Source: https://extension.umn.edu/preserving-and-preparing/canning-tomato-products-safety-guidelines
Treat all varieties and colors of tomatoes the same. They all require added acid for safely canned tomatoes. Learn more at www.bookstore.ksre.ksu.edu/pubs/MF1185.PDF.