Do you, like most readers, assume that Anthony Goldstein is an assimilated and non-observant Jew? Were that so, he could fit the Jewish law category of Jews so unaware of halakhah that their sins are inadvertent (tinoq she-hishbah bein ha-nachrim, bShab 68a-b). Otherwise, why is Anthony Goldstein the only Jew among Christians at an elite English boarding school?  
The answer may be founding in our recent daf yomi reading (bShab 75a):
“You shall not learn to act … [like a sorcerer]” [Deut. 18.9]
Nonetheless, you may learn to understand and the teach [sorcery].
This sugya (pericope) teaches us that Anthony Goldstein is only going to Hogwarts to learn about sorcery. Learning sorcery is only permitted to Jews in order to help formulate and enforce Jews laws against sorcery. Obviously, Anthony intends to return to London and teach Chief Rabbi Sir Jonathan Sacks, shlita or other Muggle Rabbis how to deal with wizards et al.
Would someone please inform J. K. Rowling about this part of the backstory to Harry Potter? She may need to work it into her next book. Tell her Kaspit sent you.
 Of course, he also needs to be capable of magic, but Jews have a long track record performing magic. Oh, and I realize that there are other token non-Christians, but only one Jew?! He must be on a fact-finding mission.
 Hat tip to the Sabbath Meals' balabusta for the tip on Anthony in my post on Harry Potter & Jewish law: Quidditch as an occupational hazard.