Does OotP destroy the H/G shipp

[blu_hermione]

No: HPFGUIDX 68383

Rereading OotP I found myself going back over Sirius and Harry's 
conversation about the marriages between pureblood familys. Sirius 
was practically related to almost every pureblood family in england 
and Harry being the son of a pureblood there could be a close blood 
relationship between him and the Weasley family. If they were second 
cousins or such the prospect of Harry having a romantic relationship 
with Ginny. Incest relationships do not seem like something that JKR 
would be in favor of therefore it might hurt the ship. Also Ginny's 
lack of romantic feelings toward Harry in this book, to the chargin 
of Ron, have put a damper on that ship. I think it might have sunk. 
Does anyone else have any other ideas
Blu_hermione