I think the "absolutist" view of antisemitism is flawed, because it can vary according to circumstances and time. During Wagner's time not as many Jews had assimilated, such as Mahler later on. Mahler himself said he couldn't relate to the orthodox Jews he observed (in his letter to Alma). Mahler was so assimilated that his very identity could no longer relate to being Jewish.
Wagner seems more irritated by the failure of Jews to socially assimilate during his time. Figures like Mahler came later. Hitler's antisemitism is more about race, and physical traits, regardless of the exceptions who had assimilated. The more jews intermarried and mingled, the more their "Jewishness" got watered-down, and softened genetically.
I think Schoenberg was totally assimilated, totally German in identity, and desperately wanted to be part of the great Germanic/Wagnerian/Brahmsian tradition, but his lingering Jewish physical traits (balding head, etc) were what was used to reject him socially. So he had to leave, as Mahler did, betrayed by his own country.
Personally, I've decided to consider Wagner seriously, with a recent purchase of the complete Ring, and I want some perspective on his "antisemitism" that is not 'fundamentalist' and absolutist. Another reason I disagree with the absolutist view is because, whether we acknowledge it or not, all humans are racist.
Whether this racism is conscious (acknowledged as a universal human trait) or not can depend on if one is part of the "status quo" or majority who take identity for granted (most white people), and those who are of a minority or identify strongly with certain identity aspects: gender, sexuality, race (blank, Asian, Hispanic), orthodox Jews, white supremacists, and other strongly-defined identity associations.
These other strongly-defined identity associations tend to make these groups more sensitive to the idea of racism, though in most cases they see themselves as victims.
Thus, everybody on both sides needs to acknowledge their own racist nature. All humans are racist; it's how we deal with it that matters. And this means talking openly and flexibly about it, and ourselves.