Does the Old Testament law prohibit marriage among step siblings? I ask because I'm trying to understand whether the prohibition against sibling marriage is due to genetic or emotional reasons.

Suppose Bob and Alice marry, have a daughter Eve, and some years later Alice dies.

Suppose Chris and Diana marry, have a son Frank, and some years later Chris dies.

Now, suppose Bob and Diana marry -- that would make Eve and Frank stepsiblings with no shared biological heritage.

Would the Old Testament law, in this case, prohibit Eve and Frank's marriage?
The prohibited forms of incest are found in Leviticus 18.

Verse 9 is of the most concern:


  9 “‘Do not have sexual relations with your sister, either your father’s daughter or your mother’s daughter, whether she was born in the same home or elsewhere.


Verse 11, however is also interesting:


  11 “‘Do not have sexual relations with the daughter of your father’s wife, born to your father; she is your sister.


Here, only children born of the father are considered. As such, a step sibling sired by another man (such as the case you posit) would appear to be fair game.

The complete list disallows:


your mother
any woman your father marries (honor)
your sister, or the daughters of either of your parents
your children's daughters (honor)
your father's wife
your aunt on either side (she is "a close relative")
your daughter-in-law
your sister-in-law


In many cases, the point seems to be "don't dishonor your family."  I suspect (and here I put on my Rabbi hat and accent), the idea would be that you could not seek out your step-siblings, but if the marriage were to occur before your father and her mother were to marry, that they would be dishonoring you, not you them.

All of this, of course, is far more legal and lawerly than Christianity normally gets, but you asks the question, you gets the answer...