UCAS privacy policy says this 'It’s up to you if you give details about your ethnicity, sexual orientation, gender identity, and religious belief – this will help providers check their compliance with the Equality Act 2010. This information is provided to your chosen provider after you’ve secured your place, or at the end of the application cycle.' so I doubt it will make any difference to your application as it seems they don't get that information until the admissions cycle is over. And as far as I know, when Oxford considers contextual factors in making offers it is specifically as it relates to education (so they consider things like your school quality and progression to HE, your neighbourhood socioeconomic status, whether you were on free school meals, spent time in care etc), so your religion is unlikely to be relevant in this regard.