Even when Bush appointed Gates, it was noted he was a moderate from academia... or something fishy.
Remember, it was when Bush was in deep shit and needed to appease Moderate Repubs and Dems.
Gates began working for the CIA when he was in college. He has served in every administration since Nixon, except Bill Clinton. He served as Deputy NSA to Kissinger, Brzenski, and Scowcroft. Reagan nominated him to CIA Director, but he had to withdraw because of Iran Contra. GHW Bush renominated him to CIA Director and he was confirmed. He turned down two jobs in the GW Bush administration before he accepted the SecDef job.
As for being a moderate, Gates is a member of the Realist Foreign Policy School which is composed of Republicans and Democrats.
When he became Sec Def for Bush he was not merely Bob Gates going to work for George Bush. That was a doctrinal shift in the Bush Administration. The NeoCons had been running Bush's foreign policy and Bush replaced the NeoCons with the Realists. Gates was the point man of the Realist boarding party taking Bush's foreign policy away from the NeoCons.
When Obama came in, he retained the Realists, including Gates. That is why you see Republican Realists like Powell, Scowcroft, Baker, Kissinger and others advising and supporting Obama.