I am not aware of fully actin independent pathways in yeast or fungi. The reason for actin begin required is thought to be connected to the fact that their plasma membranes are under tension due to turgor pressure (see Aghamohammadzadeh & Ayscough, 2009). When mammalian plasma membranes are under pressure, endocytosis also now appears to require actin (Boulant 2011). There might be pathways in yeast that have a different extent of requirement for actin (see Prosser et al, 2011 and Aghamohammadzadeh et al, 2014) but complete disruption of F-actin appears to stop endocytosis. Currently however we know very little of these alternative pathways and their requirements for other proteins such as clathrin for example.