Surely this so-called requirement to be a ordained minister of the Church must be a misunderstanding by somebody!
I don't believe that Oxford had such a requirement for teaching staff. The University runs (ran) it's own system with lecturers, professors etc. But it does require that teaching staff have an association with the "self-governing" University Colleges - typically as Fellows. So individual Colleges could have a requirement that Fellow must have at least part I Tripos (exam after 1/2 years) in Divinity. As Dodgson was a third generation at Oxford, he may have joined a "family" college with an organised Christian emphasis. Even in my day - the 60's (I went to "the other place" though - the pale blue), the entry requirement for both Latin and Greek proficiency was only just a thing of the past.
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