I don't think this is straightforward. Angrist and Krueger in their survey paper argue that 2SLS is still a robust means of estimating an average treatment effect when
the dependent or IV variable is binary. However, they don't discuss fixed effects models.
Angrist, Joshua D. and Alan B. Krueger (2001), 'Instrumental
variables and the search for identification: From supply and demand to
natural experiments' Journal of Economic Perspectives 15:69-85.