

The argument for Luke's genealogy being that of Mary is very weak. According
to Luke 3:23

   And when he began his ministry, Jesus himself was about 
   thirty years of age, being supposedly the son of Joseph,
   the son of Eli,

Aside from the fact that Mary is not mentioned, there are two possible
interpretations: either Joseph was her father or he was her brother.
Clearly this is not acceptable.  A third would be that Joseph, the son
of Eli, was her Father and just happened to have the name as the man
to whom she was betrothed. But that would seem to be grasping at
straws. The most straightforward interpretation is that Luke had no
intention of tracing Mary's genealogy (in which case he would have
named her) but that he traces her husband's, from David's son Nathan.

The Matthew descendant list most definitely traces down from David's
son, Solomon, to Joseph.  Matthew 1:16 reads:

   And to Jacob was born Joseph, the husband of Mary, by whom was born
   Jesus, who is called Christ. 

There are two apparent problems.  The first is, how to reconcile the
two paternal genealogies - which diverge with the sons of David,
Solomon and Nathan.  The second is, why is any genealogy of Joseph
relavent at all, if Joseph had nothing to do with it.  If Joseph was
not Jesus's physical father, then the original poster is quite
correct, that claims for Jesus's messianic heritage are not based on
truth but only on appearances, whatever Jesus's divine nature was.

The second problem is easy, in my mind.  We assume that Joseph was not
involved in the conception of Jesus in any way.  However, a Holy
Spirit capable of working a physical conception in Mary is also
capable of employing the physical agency of Joseph's seed in this
work.  In our materialistic times we interpret viginity and its loss
solely in terms of a physical act, whereas it is really a matter of
purity on a much higher level as well.  The important thing is that
neither Mary nor Joseph was conscious of any union between them (they
had not "known"each other).  Thus the first gospel's dedication of
half its opening chapter to the genealogy of Joseph is quite relevant
to Jesus, the Virgin birth not- withstanding.

To the first question there is an answer that creates, to begin with, more
problems than it resolves.  It is that the two evangelists are relating 
the births of two entirely different children of two entirely different
sets of parents.  Except for the names of the parents and the child, and 
the birthplace in Bethlehem there is no point in common between the two 
stories.  Matthew and Luke converge in their accounts only thirty years
later with the Baptism of Jesus in Jordan.  Rudolf Steiner offered his
explanation of how these accounts begin with two children and then converge
with their accounts of the one Jesus of Nazareth.  He did not derive his
resolution from biblical study or speculation, or from other external
documents, and the discussion of "how this could be" might bring us beyond
the limits of appropriateness for this newsgroup.  In any case, the
details are described in Steiner's "The Spiritual Guidance of the Human 
Being and of Humanity", "The Gospel of St. Luke", and "The Gospel of St.
Matthew". 

Whether or not Rudolf Steiner's methods and explanation are accepted
as valid, at least this interpretation resolves the apparent
contradictions of the two genealogies while leaving the text intact.

As for the passing of one's Jewishness through the mother, this was
never an issue with Jesus. No one ever questioned his or Mary's
Jewishness.  The issue of the genealogies has to do with his paternal
line of descent from David, the king.