The whole idea of ethnicity is a spurious hangover from the past anyway. If it depends on DNA, then what about intermarriage and adoption? If it depends on ancestry, get out that copy of the Nuremberg laws.
No need to comment on the above really. We're either all an ethnic minority (see "out of Africa" theory of human evolution, as well as "mitochondrial Eve" one), or the question is moot. Please note, this means there are no ethnic majorities either, just that we're all equal(ly human).
But, once you allow for ethnic minorities and start "helping" them out, you may easily run into the following kind of problem. I've seen it happen with humanitarian aid unrelated to ethnicity, but the foul motives are the same. What makes it even worse is that it's members of the same community that needs help that are getting fat on the misfortune of their own. It happens all to easily...
It encourages clientilism, where self-appointed “community leaders” try to grab as much as possible from the public cake, in theory for their constituents, but in practice often for themselves. That encourages ill-feeling between the “minorities” and for the “majority” which feels left out.
And finally, an almost obvious truth: the same things ethnic minorities suffer from are a problem for the majority, too, not least because they are the result of the failure of government to enact it's own laws and rules:
The biggest complaints from many ethnic minorities are really about something else: bad behaviour by the authorities. Much better, therefore, to concentrate on solving that with a clean and responsive government, good laws and a good justice system.
To finish, I also heartily agree with the article's author that there are areas where direct help and even (local) favouritism are often called for, and justified. One is language, as the author also points out. The other is the "culture" insofar as it's different enough from the mainstream to require extra(ordinary) support.
I again urge you to go and read the article itself. It is so much better than my lame attempt at both summarising it, and giving my own contribution.