It is common in speech, and not unknown in serious writing, to use they or them as the equivalent of a singular pronoun of a common sex, as in: "Each insisted on their own point of view, and hence the marriage came to an end". This is stigmatised by grammarians as a usage grammatically indefensible. It ought, they would say, to have been "He insisted on his own point of view and she on hers". Jespersen says about this:
In the third person it would have been very convenient to have a common-sex pronoun, but as a matter of fact English has none and must therefore use one of the three makeshift expedients shown in the following sentences:
The reader's heart — if he or she have any. ( Fielding).
He that hath ears to hear let him hear. (A. V.).
Nobody prevents you, do they? (Thackeray).
The official writer will be wise for the present to use the first or second, and not to be tempted by the greater convenience of the third, though necessity may eventually force it into the category of accepted idiom. The Ministry of Labour and National Service have invented another device, but it is an ugly one, suitable only for forms:
Each worker must acknowledge receipt by entering the serial number of the supplementary coupon sheet issued to him/her in column q and signing his/her name in column 5.
Whatever justification there may be for using themselves as a singular common-sex pronoun, there can be no excuse for it when only one sex is concerned.
The female manipulative jobs are of a type to which by no means everyone can adapt themselves with ease.
There is no reason why herself should not have been written instead of themselves.