The quoted passage is from R v Dudley and Stephens (1884) 14 QBD 273, a famous case because of its colourful circumstances (shipwreck, murder, cannibalism) and for its relevance to the notion of necessity at common law. The defendants, following the loss of their vessel, had killed and eaten a fellow survivor; a fourth man present took no part in the killing. Their trial for murder hinged on the question of whether there was a defence of "necessity"; that is, whether the killing could be excused because it was necessary in order for the remaining crew to survive.
The fragment of this judgment regarding women and children cannot act as precedent for there being a legal duty to prefer them to adult men in case of shipwreck. In context, it does not argue that the duty exists in law; it's being used as an example of a moral duty which should not be contradicted by an overly strong duty of self-protection. The precedential value of the judgment is what it has to say about killing others to save yourself on the grounds of "necessity". It was not seeking to establish anything about choosing which other person to save.
In the opinion of the Lord Chief Justice, Lord Coleridge, there was no defence of "necessity". The extract above is part of a longer paragraph where he argues that the circumstances of the case differ from what the legal authorities calls "necessity". The first part of the quotation is to support the conclusion, hidden by the ellipsis, "It is not correct, therefore, to say that there is any absolute or unqualified necessity to preserve one's life." That is, the necessity is not absolute because there are situations where moral duty would point the other way, and demand self-sacrifice. Although legal and moral duties do not always coincide, he claims that in this scenario, the existence of a moral duty (to sacrifice oneself to save others) means there cannot be a legal duty in the other direction entirely (to preserve ones life even at the cost of killing another).
The example of HMS Birkenhead (another famous shipwreck) is brought in to illustrate the moral principle. It was a well-known disaster, where it was generally accepted that soldiers aboard the vessel had acted morally correctly in giving scarce lifeboat space to the civilian passengers, who were predominantly wives and children of the male soldiers. In so doing, they were putting the lives of others before their own. But the example is not being used to claim anything about the soldiers' moral duties as between male and female civilians. It is also not being used to support an argument that they had a legal duty to do so. If they had one, then this would be a stronger direct argument against the necessity defence, compared to the slightly roundabout tour through morality that Lord Coleridge actually takes.
Indeed, just after this quoted passage he explicitly disclaims the idea that one life is worth more than another:
Who is to be the judge of this sort of necessity? By what measure is the comparative value of lives to be measured? Is it to be strength, or intellect, or what? It is plain that the principle leaves to him who is to profit by it to determine the necessity which will justify him in deliberately taking another's life to save his own. In this case the weakest, the youngest, the most unresisting, was chosen. Was it more necessary to kill him than one of the grown men? The answer must be “No”—
“So spake the Fiend, and with necessity, The tyrant's plea, excused his devilish deeds.”
(That last bit is from Book 4 of Paradise Lost, referring to Satan's plan to conquer the world, which he claims is a course of conduct forced on him by God's own actions.)
As for the current value of Dudley and Stephens, it continues to be cited for the non-availability of the necessity defence. These days that is interpreted through R v Howe  UKHL 4, as it was cited with approval in the speeches of Lord Hailsham and Lord Mackay of Clashfern. That is a more recent case from a higher court, on a related topic, and so that "endorsement" carries weight for anyone wondering if a Victorian precedent was still valid. Lord Hailsham, dealing with the concept of duress, said that Dudley and Stephens was "generally and, in my view correctly, regarded as an authority on the availability of the supposed defence of necessity rather than duress" and Lord Mackay said that the principle "cannot be wrong in the present appeals". The sense of the House was that primary legislation would be needed in order to bring in a defence of duress or necessity to murder, after such a long time of the opposite being held true.
A recent such citation is in an assisted suicide case, Nicklinson v MoJ  EWCA Civ 961,
Nor is there a general defence of necessity: see R v Dudley and Stephens (1884) 14 QBD 273, affirmed by the House of Lords in R v Howe  1 AC 418 per Lord Hailsham at 429B-D and Lord Mackay at 453B-F.
Even if people could get away with just citing Howe, they probably continue to include the former case in some instances just because it is so well-known.