Can leftists claim Nietzsche as an influence?

Of course! The appropriation of Nietzsche by right-wing extremists usually relies on selective reading, but any appropriation usually does. In a larger sense, Nietzsche's philosophies are far more varied than the superman stuff in BEYOND GOOD AND EVIL (the philosophy most often used to justify forced superiority). The ideas in THE BIRTH OF TRAGEDY are about how community bonds through recognition of helplessness in the face of Fate - hardly a political idea, but more akin to the community based philosophy of "leftists." And the theories of THE ANTICHRIST are hardly going to appeal to conservatives. But even in BEYOND GOOD AND EVIL, the idea of the superman transcends political simplification. He is a lonely figure, because of his greatness. Sure, he mentions "political" figures like Napolean and Alexander, but rulers like this have in fact transcended whatever ideology justified their power and are better understood through their ambitions and craze.