“I mentioned this to someone at work today and they looked at me as if I were a space alien.”
I cited one --this “one” is not the one I am talking about-- of the example sentences where “they” are used to refer to a person --for example, “someone” in the above sentence-- of unspecified sex.
If “he” follows “someone,” those who are usually called “she” are upset, aren’t they.
Perhaps they are happy to be called “they.”
When I first came to the UK, this particular unspecified “they” didn’t exist. The sentence from the Oxford Dictionary would have been stated as “ask your friends whether they can help” or "ask a friend whether he can help.
As you imply, this use of ‘he’ became anathema to some “theys” in the feminine movement and ‘one’ could easily get into hot water over it. Gradually the ‘they’ took over, first in the spoken language. The once ubiquitous ‘he’ became “he or she” in writing and, a little later and less formal “s/he”, something which wasn’t approved of by the "he"s in our company. These days, the ‘they’ is used quite extensively in writing, too.
In your above example, I would still prefer the correct pronoun. After all, one would know whether one had spoken to a “him” or a “her”. Unless . . .?
N.B. I am overdoing the ‘one’ on purpose: one just wants to illustrate the use of formal language. If anyone objects, ‘they’ can always look away