In this case, its pretty easy.
If you say he's a bad President with bad policy decisions and poor judgement, that's the content of his character (or actions). If you say he's a (sand) nigger or muslim or mention slavery or his non-whiteness, as many of those posts in the blog did, its racist. If you talk about the preferred method of assassination being lynching as MANY of these did, its *really* racist (also stupid as shit).
Those were *really* blatant. "I'm not racist!" one said, "I like plenty of black people, I just hate niggers" (paraphrased by me, site's down now). Its hard to read that as anything but, "I like the black people who know their place, i.e., subservient to my white ass." And that'd be one of the nicer ones.
Things get fuzzier when you have someone talking about the loss or waning of "Traditional America", which is IMO racist -- but which is trying very hard to cover it.
When you talk about the only reason he won is because the "new" America is getting "gifts" from Santa, you're bemoaning the decline of the white male bloc and rather offensively deciding no one but that white male bloc can make an intelligent decision on its merits -- that's just generally insulting, but arguably not quite racist. But is it *damn* close to both racism and male chauvinism (since this new America also happens to include whores and sluts: i.e., single women who are thinking only of sex sex sex sex sex sex and all the sex they can have for free now, and not about the future as a responsible wife and mother would).
Sure there are plenty of people who are Obama critics who are not racists. However, a LOT are -- and a LOT of what's going around is very thinly veiled racism. This blog was posting up stuff which didn't even try to veil said racism, though. :)
When a frankly moderate (at best: we progressives did /not/ get the far-left guy we thought we wanted) President's every action is treated as some sort of alien insurrection that is utterly incomprehensible to the people -- there's something more then just policy disagreement going on. It's so far beyond partisan or political policy.