Confused about the relationships between Leo Strauss, neoconservatism, and the "new Right"

[Aurelius]

Leo Strauss is often considered a father of neoconservatism alongside Irving Kristol. But he's also a favorite philosopher of the heterodox "new right", especially the Claremont folks (but certainly not exclusive to them), and one of their defining characteristics is opposition to neoconservatism. What am I missing here?

[Statilius the Epicurean]

I wouldn't see Bush-era Neoconservatism and the post-Trump "New Right" as entirely oppositional. Perhaps some on the right would like to forget it now, but the Bush administration's foreign policy was fundamentally unilateralist and "America First" - invading Iraq in defiance of the UN and international community the obvious example of this. Victor Davis Hanson is one Bush-era "neocon" at the Claremont Institute who later became a prominent intellectual advocate for Trump, without changing many (any?) of his views.

At any rate, Leo Strauss taught the transhistorical value of Great Books, that political and philosophical wisdom was the preserve of an elite few, and that the Enlightenment project led to nihilism. Not difficult to see why different strands of conservative thought would be attracted to him.