Influenza virions are enriched in cholesterol relative to the plasma membrane from which they bud. Previous work has shown that fusion between influenza virus and synthetic liposomes is sensitive to the amount of cholesterol in either the virus or the target membrane. Here, we test the chemical properties of cholesterol required to promote influenza fusion by replacing cholesterol with other sterols and assaying viral fusion kinetics. We find that influenza fusion with liposomes is surprisingly robust to sterol chemical identity, showing no significant dependence on sterol identity in target membranes for any of the sterols tested. In the viral membrane, lanosterol slowed fusion somewhat, while polar sterols produced a more pronounced slowing and inhibition of fusion. No other sterols tested showed a significant perturbation in fusion rates, including ones previously shown to alter membrane bending moduli or phase behavior. Although fusion rates depend on viral cholesterol, they thus do not require cholesterol's ability to support liquid-liquid phase coexistence. Using electron cryo-microscopy, we further find that sterol-dependent changes to hemagglutinin spatial patterning in the viral membrane do not require liquid-liquid phase coexistence. We therefore speculate that local sterol-hemagglutinin interactions in the viral envelope may control the rate-limiting step of fusion.