The name Stadler is one of diverse origin, one that began in different locations independently, so a Stadler family from one part of Germany might or might not be related to another.
It is now possible to know if any Stadler family is related to another Stadler family. The pattern in a man's Y Chromosome is inherited only from his father, it may make small changes and over time there have been enough changes to tell one family from another.
My Statler Project includes the name Stadler and although the original goal was to test families who were in America before 1790, any male with a Stadler name is welcome to join. At this time we have one participant whose ancestor came from Germany in the 1850s.