Thanks, everyone, for all the replies.
After giving it some thought, I think both genes and culture are important. And I think I can prove my point by mentioning all the many clubs in The Villages that depend on a combination of genes and culture: Irish, Italian, German, Mexican, Filipino, African and others. (Sorry if I left out any group.)
Try telling all those people that genes and culture don't matter.
Here's a real life example that I experienced not too long ago. I'm not Irish but out of curiosity I decided to go see the Raggle Taggle Band in The Villages. They play Irish music almost exclusively. Anyone can go see them but I think the people in the room were about 99% Irish. (Or it might be more accurate to say "Celtic"?)
If it doesn't matter or people don't care about culture and genes, what was that gathering all about? You could see that they shared a similar Irish look (genetic) and the music represented their Irish cultural heritage. They share a special bond that's not exactly the same as what they share with others. The same goes for Italians, Germans and other ethnic or racial groups.
I'm not suggesting that we all go around calling ourselves Italian-Americans or Irish-Americans etc. but we shouldn't be in denial of who we really are.
Therefore, I say the pope's genetic and cultural heritage should not be dismissed.