Why is Keynes attacking the (neo)classical theory of interest rates on the grounds that it is indeterminate?

You can use some some initial $Y_0$ to find an interest rate, but this is precisely the indeterminacy problem. We would like to be able to derive the equilibrium interest rate without assuming some initial values.

Furthermore, note the indeterminacy problem is actually present even in canonical Keynesian models (See Hansen, 1951) and Neo-Keynesian models (see Beyer & Farmer 2004).

However, the Keynes critique is now a bit outdated. Keynes was writing in a past before macroeconomic was even given proper formal treatment (by modern standards), and at a time when macro had no micro-foundationds. Nowadays you can solve the indeterminancy problem in macroeconomic model of either variety by assuming central bank follows some interest rate setting rule, such as Taylor rule or making some specific assumptions about model's micro-fundamentals (see Romer's Advanced Macroeconomcis for discussion of this). Although as the Beyer & Farmer point out in their paper even central bank interest setting rules won't solve this issue always so the problem is somewhat open.