'Blood carries' is obviously true. I have the same color skin as my parents. The concept is not archaic, intellectually offensive or dangerous. It's also in no way connected to racism.
> I sit here, armed with this knowledge, and I think to myself quite shamefully, You can take the man out of Syria but you can't take Syria out of the man.
Seems like author is punishing self for some relatives faults. There is absolutely no reason to feel shame in this case, in my mind.
Though I wouldn't say it would carry enough of a personality trait to be able to use the term seriously.