My vague assumption was that they would be looking for students with strong evidence of linguistic aptitude - in other words, it would be the elimination of the language requirement at GCSE, with consequent fewer numbers taking a language A-level in state schools, which would be the biggest obstacle for candidates from the state sector. This seems not to be the case.
According to the relevant page on the OI website, even an A-level in an Oriental language offers no significant advantage:
All undergraduate degrees in Oriental Studies involve the teaching of difficult languages from scratch, since only in exceptional cases will students have studied the languages before coming to Oxford. Our experience has been that an A level in an Oriental language does not give significant advantage to a student, since the Oxford courses involve such a broad range of cultural elements in addition to language study. The progress of language learning from the start of the B.A. course is so intensive that the majority of students beginning from scratch find that they quickly catch up with those who may have some knowledge of the languages from school or family background.
In other words, you might think, this could be a good choice for a student from the state sector, because the Oriental Institute has had to assume responsibility for teaching all students to a high standard from scratch. Students are offered a linguistic aptitude test which you can try out here (solutions here); the test seems to be designed to test whether you can get the hang of an inflected language in which word order is no guide to sense, a challenge for which five years of French, say, would offer no great advantage.
Oddly enough, though, the things that really count seem much harder for someone from a school for students of widely varying abilities to demonstrate.
We judge whether you should be offered a place to study an Oriental subject at Oxford according to the evidence presented to us in your admissions documents: your UCAS form and the written work which you submit, plus our assessment of your potential during your interview. (Some subjects may also set an informal test during the interview.) We would expect successful candidates to demonstrate the following: high academic achievement, great potential for the intended course of study, good work habits, international outlook and strong motivation. Oriental Studies courses require a) a capacity for hard and well-organised work; b) the motivation to tackle languages which in most cases will be radically different from languages learnt previously and c) skills of analysis, argument and description for essay writing on an unfamiliar culture.
When I say it's hard for someone from a school with a population of widely varying abilities to demonstrate these qualities, I'm looking back to the schools I went to along the way; in this sort of school, if you hand in a piece of written work that is coherent, correctly spelled and grammatical, you will get an A.
Teachers are not going to give challenging assignments, because they don't want weaker members of the class to be demoralised. They are not going to hound the A student for inadequate skills of analysis, argument and description. And they're unlikely to set large numbers of written assignments in any case - the kind of thing that would require a good student to develop excellent work habits - both because, again, they don't want weaker students to be demoralised, and because it's hard work labouring through large numbers of papers that are incoherent, poorly spelled and ungrammatical.
A student in this kind of environment who has high academic potential is not necessarily going to have much in the way of a track record of achievement; he or she is likelier to do what I did, hand in schoolwork as required, be very bored, spend a lot of time reading. Such a student would be doing well to achieve the necessary A grades at A-level; I don't know that he or she would be likely to offer anything very impressive as supplementary material for an application.
I do realize, of course, that a university must have some criteria for selection. It may be that it's simply more straightforward to devise a programme for intensive language teaching from scratch than it is to teach, I don't know, excellent work habits, an international outlook and powers of analysis and argument. And yet...