starter - well I’ve no idea about Oxford, but just looked at the stats for Cambridge which are freely available. Some variations between colleges, but overall for 2019, 72% of all applicants were from the state sector. Of all offers made, 71% were made to the state sector (so roughly proportional). And of offers accepted after results were published, just under 69% were from the state sector (roughly what you would expect given that, every year, a few will not make the grades in the actual A-levels).
Yes, there is an argument that the number of state applicants should be proportionally higher in the first place, but there’s no evidence of state applicants who do apply being disproportionately squeezed out, as far as I can tell. The uni can’t make offers to more state students than actually apply.
Also, not all independent schools are selective and not all state schools are comprehensives (grammars for instance, or selective sixth forms). It would be interesting to see the breakdown of applicants to offers for selective schools in both sectors in relation to offers made, but this is not available.,