That would not exactly be the case.
Looking at that wikipedia definition, because that cultural group in subsequent periods included the Irish (aka "wisps") … the Irish were certainly discriminated against.
But again, confining the discussion to more recent WASP culture, as per part of that definition having "inherited wealth" … I think in nearly all societies, wealth insulates you from certain degrees of discrimination … but being "insulated" does not necessarily equal "indifferent".
Re: your statement …
"It is puzzling to me why , when a family escapes their "ethnic" background and acheive upper middle class status they gradually take on all the trappings of WASPishness – especially an indifference to the plight of others not as fortunate as themselves."
Much of my more immediate family is very "upper middle class" … yet we are Italian, (with some Irish at the fringes} and very "immigrant" … however we have not "escaped our ethnic background" … we celebrate it (and quite a bit at that I might add. <ahem>)
And I don’t think that all people who achieve upper middle class status take on an indifference to the plight of the less fortunate … that idea a complaint hisorically aimed at people in higher socio-economic classes … and a "bash", as it were, that has been going on for ages … the problem is that such ideas are stated as absolutes … and such absolutes are just not accurate.
As an example, just how accurate is it to bash the poor suggest that all poorer people are wholly criminals?
Other things play into that mentality too. There are other issues of human nature where people dislike others who have more than they do in general … especially if they have pain in their lives stemming from being poorer, or outright poverty.
Displacing anger on others happens all the time … and a common way to express such antagonism without sounding too badly is to bash a group as a class … bashing the rich … bashing the poor … bashing Arab-Americans … whomever.
Every member of a group is, of course, an individual.
It would be more accurate to say that as a whole, society could do more to alleviate the problems manifested in the poorer segments.
But it is not accurate to bash a person for being a WASP any more than bashing other legitimate groups in society.