I recently read this article regarding the demographics of Reddit users. It would be interesting to see similar data for this forum. Particularly it would be insightful to see data on: location, age, gender, politics and religion. If I recall correctly, no demographic information is asked of users upon signing up, so it may be the case that there is no such reliable source for such data.
As far as I am aware, such data is not collected or stored (as you already mentioned). You can see what data Stack Exchange has of you by submitting a request. Here are some things that may give you some interesting insights, especially if you want to work through the data yourself:
Religion: you may be able to get some coarse results by figuring out what users have (active) account on the Christianity, Hinduism, Islam, Mi Yodeya, ... sister sites. I suppose the SE data explorer can give that kind of information.
Location: you may be able to infer some rough time zone details by checking when users are active. You could also check the domain names of home pages in user profiles or the existence of profiles on sister sites for other languages.
Background: this post contains a (presumably incomplete / outdated) list of users with an academic background in philosophy.
Age: users should be 13 years old (or 16 in the EU). However, this is not actively enforced.