"Neoliberal" is a term reserved for post-New-Deal-era proponents of laissez-faire capitalism.
I think what you mean are "Neoconservatives", which is the most adequate term for the pro-interventionist "liberal hawks".
This is nothing new at all, Franklin D. Roosevelt, Harry S. Truman, John F. Kennedy and Lyndon B. Johnson all were described as liberal haws.
"Left" and "right" may be used to describe social liberalism vs authoritarianism or economic pro-regulation leftism vs. pro-market rightism.
There is, of course, the pacifist strand on the left and its jingoist antagonist on the right.
It is not much disputed that there has been a pro-market anti-regulation anti-tax anti-interventionist (economically) wave from the late 70s well into the 21st century. Since these policies cause long-term instability due to their tendency to increase inequality and social disruption, especially in combination with globalization and technological innovations, momentum has been building for the pendulum to swing back to the left.
Take a look at the platforms of Democratic presedential candidates like Bernie Sanders or Elisabeth Warren, they are quite obviously to the left of the "third way" Democrats (or social democrats in Europe).
In the US this shift happened before (FDR), and - if democracy is allowed to run its course - is poised to be happen again.