  We examine the linear density contrast at collapse time, $\delta_c$ for
large-scale structure in dynamical dark energy cosmologies, including models
with early dark energy. Contrary to previous results, we find that as long as
dark energy is homogeneous on small scales, $\delta_c$ is insensitive to dark
energy properties for parameter values fitting current data, including the case
of early dark energy. This is significant since using the correct $\delta_c$ is
crucial for accurate Press-Schechter prediction of the halo mass function.
Previous results have found an apparent failing of the extended Press-Schechter
approach (Sheth-Tormen) for early dark energy. Our calculations demonstrate
that with the correct $\delta_c$ the accuracy of this approach is restored. We
discuss the significance of this result for the halo mass function and examine
what dark energy physics would be needed to cause significant change in
$\delta_c$, and the observational signatures this would leave.
