With a large percentage of the population overweight or obese, and obese men at particular risk, isn't that fact that obese men can have elevated oestrogen of interest?
The hormone is only one half of the equation, the other half is receptors. Oestrogen doesn't function like an antiviral - directly preventing virus replication/cell egress, it produces physiological changes which may offer a protective effect. In obese men, those receptors are insensitive, disturbing the hormone homeostasis and causing the body to compensate.
And does anyone know why it's oestrogen being looked into as protective while it doesn't seem to be that testosterone is being looked at as a risk factor?
There are studies looking into this too. However, the number of men in the UK who have a clinical diagnosis of low testosterone is a tiny fraction of the population or even compared to the number of women on HRT and there isn't a clear profound change that relates to testosterone levels in older males as there is with oestrogens and menopause.
And certainly questions about your reproductive system are personal!
Again, that is why they offered the option to not give an answer. It's an electronic survey, not a human interviewer, it's hardly getting a kick out of your reaction at being asked a personal question.