[I know it's been a while since I've posted, and I won't bother giving excuses. :-) ]
"Yichus is like a bunch of zeros - it's meaningless unless you put the 'one' in front of it."
The point is simple: Whether or not you come from a wonderful, frum family that has been steeped in yiddishkeit for generations means nothing if you are not committed to continuing that sort of lifestyle.
"He comes from a great family! His father and grandfather learned in Yeshiva X, his great-grandfather was the Rabbi of such-and-such town in Russia, and his mother's whole family have been the cornerstone of American Jewry for decades! The boy? OK, well, he's a yeshiva dropout. Plans? Oh, he doesn't have any... No, he isn't all that interested in a family..." Obviously, that was an exaggeration. But the principle is the same - you don't marry someone based on their family.
Now, allow me to interrupt myself and say very clearly; Family is an extremely important factor to consider when dating for marriage! I am a huge believer in that. True, you marry the person him/herself, and not the family. But that doesn't mean that you won't interact with your spouse's family. That doesn't mean that the person you are suddenly spending the rest of you life with hasn't been influenced (for both the good and not-so-good) by their family for twenty-something years. It is impossible to ignore the impact of family on a spouse and future married life.
So yes, family is important, but not exclusively. But to get to the real question; What if the situation is flipped? If the family is not so stellar, but the boy/girl in their own right is a committed and really great ben or bat Torah?
This is a topic that has come up on numerous occasions at my family's Shabbos table, with regards to dating the children of ba'alei teshuva or gerim. The debate is usually split into two camps: my parents, (who both come from frum committed Torah families) while welcoming ba'alei teshuva and gerim into the Jewish community and marveling at their journey, at the same time would rather see their children married to the son/daughter of families similar to theirs. With families of ba'alei teshuva/gerim, they admit to having some reservations. My parents don't think any less of these Jews for having different backgrounds - they just aren't entirely comfortable with the idea of non-frum/non-Jewish in-laws, or even ancestors.
While we understand where our parents are coming from, my siblings and I think a little differently, and are not so cautious with the idea of dating someone from such a family. If the person suggested by a shadchan "makes sense" regarding what we are each looking for (in terms of Torah lifestyle, plans for future, desire to build a Jewish family, etc.), then we would be totally fine giving that person from a BT/ger family a fair chance, like anyone else.
My question for readers is, how far should it go? Let's say a solid, frum boy/girl who's grandfather was a ger is suggested to you - should that be a "deal-breaker"? What if you gave it a chance, and it began to get serious? Would you break it off because it might possibly cause machlokes with your family? (Don't laugh - I know someone who did this - don't worry, she's happily married now!) If the "one" is a really worthy "one," how much importance is granted to the "zeros"?