"Women and children first" is not a principle. It's a conclusion which emerges from principles.

There were many "Christian" men survivors from the Titanic, but most men went down, many who were probably non-believers. 
I still give up my seat to women on the sub-way. It is a matter of upbringing, not faith. m/r

Would an Atheist Give Up His Seat on a Lifeboat? | PJ Media

by Walter Hudson  January 24, 2016

Does your belief in God affect whether you are willing to give up your life on behalf of another? A caricature of atheism exists among theists which imagines the former as unchecked hedonism and moral relativism. Ayn Rand, one of modern history's most prolific atheist writers, often bears that caricature. If popular impressions of Rand were true, you would expect her to muscle her way past others in a soup line. Because Rand claimed that a person's own life should be his or her highest value, her critics frequently paint her as a heartless grinch who scoffed at the suffering of others.

Reader Geoffrey Britain echoes that in his response to an Objectivist explanation for the origin of rights without God. He comments:

The author and Ayn Rand to whom he looks, state, "To hold one’s own life as one’s ultimate value, and one’s own happiness as one’s highest purpose are two aspects of the same achievement."

That statement is antithetical to Christ's declaration that, "Greater love hath no man
than this, that a man lay down his life for his friends." Since laying down one's life for a mere friend is to place the preservation of their life above one's own.
...

Rand's philosophy' denies humanity's very survival, since by her 'moral calculus' "women and children" do NOT come first but rather its every man for himself.

If Britain's impression of Rand were accurate, he would be right to condemn her. But Britian's impression is not accurate. ...

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