There are a few things to keep in mind:
1) Ariana Miyamoto was chosen as Miss Japan by Japanese people.
2) The critics of Miyamoto are an extreme, vocal minority on Twitter and 2chan.
3) Although Japanese contestants often perform well at the international level, beauty pageants of this sort do not receive much attention within the country regardless of the contestant.
4) "Hafu" is a Japanese word derived from the English "half". It is used to refer to biracial people, but there is no connotation that they are "half" a person. I cannot understand the logic of the author who says that the word sounds derogatory in English -- it's a Japanese word, after all, and is not derogatory in Japanese.
The author uses point (2) as well as his short personal experience in Japan to make broad statements to the effect that Japanese people in general do not accept those whose appearance differs from their own. Japan makes an easy target in this regard because of the well-known (outside Japan, at least) concept of Nihonjinron, as well as the persisting sense that Japan is an isolated country where outsiders will never be accepted into the "in group". Due to this, there is an expectation (particularly in foreign media) that Japanese are racist, and any proof, even that of an extreme minority on Twitter, is taken as evidence in support of this.
Of course, living in Japan, I remember hearing similar broad statements about racism in the United States concerning the backlash against electing a black president in 2008.
The real lesson here is that we should not be basing our impressions of an entire society on a vocal minority, no matter how much their opinions conform to our expectations.