The “social aspect of libertarianism” varies widely from person to person.
On abortion they split on the extremes...but the national Libertarian party attempts a compromise that is just plain silly, and is essentially pro-abortion.
Frankly, I don't get how the Libertarians support abortion.
The choice argument as put forth by both Libertarians (big-L) and social liberals has a glaring flaw: by choosing to engage in sexual activities that carry the inherent risk of pregnancy, the woman is implicitly choosing to accept that risk. And, as such, if she voluntarily chooses to engage in activities that could potentially lead to pregnancy, she must also simultaneously accept the personal responsibility that is inseparable from her choice. And, if the woman is not of legal age, the responsibility for properly informing the woman, as well as the responsibility for the woman's failures, ought to fall squarely on the heads of her parents or legal guardians.
That said, this argument fails when you consider cases of rape and incest; that's where the waters really are murky.
If a fetus is killing it's mother for whatever medical reason, it's up to the mother if she wants to give her life to her unborn child, or to prevent her own life from being taken.
No matter where you come down on this one, the FedGov has ZERO authority to either forbid or mandate abortion or the financing thereof.