  We investigate the effects of a $Z_2$ symmetry in the CP-conserving
Two-Higgs-Doublet-Model (2HDM); which is often imposed to prevent
Flavor-Changing-Neutral-Currents (FCNCs) at tree-level. Specifically, we
analyze how a breaking of the $Z_2$ symmetry spreads during renormalization
group evolution; employing general 2-loop renormalization group equations that
we have derived. Evolving the model from the electroweak to the Planck scale,
we find that while the case of an exact $Z_2$ symmetric 2HDM is very
constrained, a soft breaking of the $Z_2$ symmetry extends the valid parameter
space regions. The effects of a hard $Z_2$ breaking in the scalar sector as
well as the stability of the flavor alignment ansatz are also investigated. We
find that while a hard breaking of the $Z_2$ symmetry in the potential is
problematic, since it speeds up the growth of quartic couplings, the generated
FCNCs are heavily suppressed. Conversely, we also find that hard $Z_2$ breaking
in the Yukawa sector at most gives moderate $Z_2$ breaking in the potential;
whereas the FCNCs can become quite sizable far away from the $Z_2$ symmetric
regions.
