We can wonder and debate ad infinitum as to why Hillary was rejected in this election, but my question is this: Why did her own party reject her in 2008?

"debate ad infinitum."

Nah, I don't know if it were so much as a rejection of her as it was getting beat by superior politician and campaigner in the form of Barrack Obama. He neutralized her "first woman POTUS" by becoming the "first Black POTUS"  Just bad timing and bad luck on her part.

a) The anti-Iraq war sentiments were so strong among Dems. She committed the cardinal sin of voting to support the Bush war.  
b) She admitted to be a mediocre campaigner, pitched against a far superior Obama.

I always felt she was the fall back option. Qualified enough in there mind but just zero magnetism or pizazz.  

... my question was sincere in that the current debate revolves around whether this was a rejection of Hillary as a person or a rejection of the Democratic Party's policies. So what was it about her back then?

Obama voted against the Iraq War.

She had a great deal of support in 08 and she came close to being the candidate that year.  In primary states they were very close with Ms. Clinton doing a bit better.  But in caucus states the Obama campaign had a better organization effort.  
So Obama became the candidate

she wasn't the candidate

Once by an unknown Senator from Illinois.

Every single county in WV voted for Trump and you'd argue it was due to the war? That's silly. It was all about the economy and trade and immigration.

gibberish and tortured logic