The path of those who fail to follow the example of scripture is often dark indeed. In particular, in referring to singular quantified entities of indefinite gender, the King James bible and William Shakespeare agree in recommending the pronouns they, them, themselves ("Shakespeare used they with singular antecedents so there", 1/5/2006; "Is 'singular they' verbally and plenarily inspired of God?", 8/21/2006; "'Singular they': God said it, I believe it, that settles it", 9/13/2006; etc.). But many people have become convinced that this is wrong; and as Horace put it, in vitium ducit culpae fuga ("avoidance of error leads to fault").
In particular, it leads to things like these:
"Everyone who calls oneself Catholic will also have to keep the principles of the Catholic faith." [Archbishop Gerhard Müller, Prefect of the CDF, quoted here]
How to convince a teammate, who sees oneself as senior, to learn SVN conceptual basics? [link]
The typical nurse who thinks poorly of oneself is likely to sabotage, snitch, and figuratively 'stab coworkers in the back' to deflect attention away from any shortcomings that he or she might have. Nurses with low self-esteems are all too ready to throw their colleagues under the bus to make themselves look better, even if the effect is short-lived. Thus, the nurse who has a low opinion of oneself is problematic to the rest of us. [link]
The Progressivist vision is to create a new American person who no longer strives to better oneself but accepts one's station in life — and looks to government to help cope not only with difficulties but with every important personal decision. [Paul Ryan, Young Guns]
It's true, as MWDEU says
This use of themself is similar to the use of they, their, and them in reference to singular terms… Such use of they, their, and them is old and well established, but this use is not.
Singular themself is certainly out there, however:
How can anyone who calls themself a conservative possibly vote for Newt Gingrich when he supported the bailouts and took 1.5 Million dollars from Freddie Mac. [link]
Membership is open to anyone who considers themself a philosopher, professional or otherwise, and who considers themself a Christian. [link]
This gripping and disturbing book should be read by anyone who finds themself revering a spiritual teacher. [link]
And the substitution of oneself, in my opinion, is much more jarring. In fact, I feel that in my own idiolect of written English (or spoken English, for that matter), things like "The nurse who has a low opinion of oneself" (where oneself refers to the hypothetical nurse) are flat-out ungrammatical.
However, similar things have been around for a while:
Anyone can satisfy oneself very easily that a slight variation in the tension of the spring will not only alter the length of the spark, but also change the electrical excitability of the cathode, and so influence the remaining molecules within the tube, and consequently the X rays. [Proceedings of the Royal Philosophical Society of Glasgow, 1897]
Anyone can demonstrate on oneself in a warm bath the relation Poupart's ligament bears to the conjoined tendon. [Pacific Medical Journal, 1897]
But then again, there are cases like this:
To be an Ishmael with one's hand against everyone because everyone's hand is against oneself, requires chiefly physical courage; but to be a writer of a book that will probably offend not only the supporters of his own class, but the members of the House who were gradually beginning to avow their belief in the nobility of one formerly exciting their hatred, was an act of high moral courage, and could only have arisen from strong conviction of the necessity for so writing. [Constance Plumptre, Studies in Little-Known Subjects, 1896]
[Note: This post started from the Paul Ryan quote, cited in Gail Collins, "Veeps wielding pens", NYT 7/18/2012]