They are not even aware Kristol voted for Hubert Humphrey for president, are they?
Yes, the left wing Democrat candidate for president in 1968 and the founder of the Minnesota Farmer Labor Party.
Humphrey had a tradition of wishing to expand federal power and influence both at home and abroad, and so Kristol favored his leanings as they conformed to the already established neoconservative movement that continued to permeate both political parties.
The neocons tend to travel where the power resides, and then influence it from within - regardless of party affilition.
Nixon had neocons, as did Carter. So too did Reagan, though they later professed upset over Reagan's smaller government bent and lukewarm internationalism. Bush Sr. was more in line with neoconservatism, as was Clinton. The Bush administration gave much safe harbor to the neocon influence, and now so too does the Obama administration.
Please expand you too limited understanding of this important socio-political philosopy that has permeated our nation's politics for decades - long before Kristol's public declarations of what neoconservatism was in the 1970's.
Perhaps the single most "neocon" president in our history was none other than FDR...