This isn't merely a consequence of the perpetual battle between blacks and Jews over who is the most oppressed pushing Jews away from black identification. Since the turn of the millennium, the survey has included a more detailed question about racial identity that includes 16 possible answers rather than the survey's traditional three. Among Jews (n = 361), 95.3% chose "white". And of course some percentage of Jews who identify as non-white trace their ancestry back to places that virtually no one considers white, like Ethiopia.
These results are not the consequence of artificially separating religious Jews from from secular ethnic Jews, either. The following table provides a breakdown by theistic orientation among the Jewish sample referenced above:
Here, for comparative purposes, is the theistic orientation of those who identify as Protestant or Catholic (n = 15,121):
While the assertion that Jews tend to identify as non-white may be the muttering of a madman (and surely of a mad man!), the assertion that the irreligious descendants of Jews tend to consider themselves to be Jewish is a reasonable one.
GSS variables used: RELIG(1-2)(3), GOD(1-2)(3-5)(6), RACE, RACECEN1