The reason religion is so powerful

[Mister Agenda]

That's an excellent question. If I had to make a choice, I would save the baby. It's not unlikely the elderly person would want me to save the baby too. All stories must come to an end, and I personally would rather have mine wrapped up a few pages sooner than I planned than live with the knowledge that my survival came at the cost of someone with their whole life in front of them.

I think the reason we would choose an infant over an elderly person (and you hinted at something similar) has something to do with Thomas Nagel's famous argument: Death is evil insofar as it deprives us of life. Therefore, the younger you are the more life you can be deprived of, and the more tragic the death. And abortion, I would argue, logically deprives an organism of the most life possible.

ps. I hadn't thought about your pregnant vs nonpregnant scenario before, and I think its a question that reinforces my object permanence argument, given that a pregnant woman can be visualized in a way that an embryo cannot. Therefore, I suspect that someone who would be fine with a two-month abortion on paper, would nevertheless be inclined to save a woman that is pregnant over her twin sister that is not.

What about the baby vs. the viable embryo in a tube?

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it's something a fetus lacks.

Do you have an argument for why this is so? Or is it something you just know?

How would you persuade someone of this?

I know this question wasn't directed at me, but: To the same extent that I know a rabbit doesn't have full personhood because its brain isn't capable of undertaking person-level activities, I know a fetus with fewer brain cells than a rabbit isn't yet a person. The only way to argue that a fetus is already fully a person is to bring in supernatural qualities that can only be claimed, not detected. If justifed belief is knowledge, my position has that justification while the opposite position is based on nothing that can be verified at all.

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In the event of a fire, you would save your [emphasis added] 5-month-old baby over a stranger [emphasis added] 5-minute old fetus as would just about everyone else.

Are you familiar with confounding variables? Your addition of kinship is one such example. Any novice scientist would know to control for such a variable, or would otherwise properly incorporate it using a two-way analysis of variance (ANOVA).

So make it your 5-minute old embryo vs. a stranger's five-month old baby. What's your answer then?

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(Note that my object permanence argument also predicts this outcome.)

On the object permanence matter, assume the embryo is in a transparent tube and you can see it, while the baby is in a crib out of sight and someone has only told you where it is. And there's a chance the baby is already dead.