Was Leo Strauss a right-winger?

I think the best answer to your question is that Strauss was anti-political ideology of any stripe or–in the spirit of your title–”anti-wing.”

Regarding Smith’s book, while it provides the needed anti-dote to the scurrilous “fascist” charge begun by Burnyeat and picked up by the left-wing press, I am afraid that it goes over board the other way. Thomas Pangle (who may be the pre-eminent Straussian today, along with Harvey Mansfield) and the Zuckerts are also coming out with a study of Strauss, and perhaps we will find a more balanced perspective there.