At the time, Oxford was indeed very, very sexist, although certainly not unique in that way. It was a different society from the one we have now. Note that the female students mentioned would not have been able to gain a degree at the time - that only became possible in 1920. Even their limited status was controversial enough that it was important to avoid impropriety, as opponents of women's education were suspicious of their effect on the male students and faculty. They had to be seen to be behaving respectably and certainly not having illicit sex with young men.
The Wikipedia article cites the story to J.R.R. Tolkien's Double Worlds and Creative Process: Language and Life by Arne Zettersten (Palgrave Macmillan, 2011), which further quotes an anecdote in The Tolkien Family Album by John and Priscilla Tolkien (HarperCollins, 1992), as follows:
He was interviewed by the head of St Hugh's: years later he described her as a formidable woman, dressed in the style of his grandmother, buttoned top-to-toe in an ankle-length dress. He remembered the severity of her expression as she enquired, "Are you married, Mr Tolkien?", and her relief at his reply. Thus Ronald gained some employment tutoring her students.
This would have happened between Tolkien's arrival in Oxford at the end of 1918, and his departure for Leeds in 1920, so the interview must have been with Eleanor Jourdain, who was particularly strict in discipline. At the time, St. Hugh's, like the other women's colleges, operated strict "chaperon rules" concerning how and when women were allowed to be in male company. You can read about this in The History of the University of Oxford, volume 8, chapter 13 ("Women" by Janet Howarth; ed. Brian Harrison, OUP, 1994), which chronicles their detailed development, selective enforcement, and protests. As of 1919, the rules included:
[Women] must not, among other things, enter men's rooms nor go to the theatre with a man without their principal's permission and a chaperon approved by her, nor go to a cafe with a man, nor on the river, nor for walks, bicycle or motor rides unless with principalian permission and at least two women in the party. Mixed societies required permission, to be renewed annually, from the women principals as well as the proctors, and meetings in men's colleges must be chaperoned. Mixed parties in cafes were allowed only between 2.00 and 5.20 p.m.
These strictures were motivated by wanting women to be seen as respectable, and in particular to shield them from sexual life or the hint of impropriety. Being alone with an unmarried man was a potential source of scandal. At St. Hugh's, a woman could receive a male visitor in her college rooms, but only so long as he was her father, uncle or brother, it was in daylight hours, and she dragged her mattress into the corridor for the duration.
As a tutor, Tolkien would have mainly received students at his home on Alfred Street: he moved there for that reason. A female student coming to his house, where his wife was also present much of the time, would be acceptable - compared to the student visiting an unmarried fellow in his college rooms, for example. The setup made it respectable enough for Jourdain to feel comfortable with the arrangement.
