Woodrow Wilson’s grandparents all came over after the Revolution. He was born a Southerner, and more of his ancestors were Scots or Scotch-Irish than “Anglo-Saxon.” Yet in a lot of ways he was definitely a WASP — or extremely WASP-adjacent. You didn’t get to be president of Princeton in those days if you weren’t considered to be a WASP.
The classic WASP was from the Northeast, but there was some “fluidity.” C. Douglas Dillon, Treasury Secretary to JFK and LBJ, was definitely a WASP (Groton, Harvard, investment banking, multimillionaire, French chateau, art collection), but his grandfather was a Texan (and Jewish).
Yes, WASP began to morph into “upper Ivy League (Penn excluded)”, leaving the door open for “passing.”