  X-ray and MeV polarization can be powerful diagnostics for leptonic and
hadronic blazar models. Previous predictions are mostly based on a one-zone
framework. However, recent IXPE observations of Mrk~421 and 501 strongly favor
a multi-zone framework. Thus, the leptonic and hadronic polarization
predictions need to be revisited. Here we identify two generic radiation
transfer effects, namely, double depolarization and energy stratification, that
can have an impact on the leptonic and hadronic polarization. We show how they
are generalized from previously known multi-zone effects of the primary
electron synchrotron radiation. Under our generic multi-zone model, the
leptonic polarization degree is expected to be much lower than the one-zone
prediction, unlikely detectable in most cases. The hadronic polarization degree
can reach a value as high as the primary electron synchrotron polarization
during simultaneous multi-wavelength flares, consistent with the one-zone
prediction. Therefore, IXPE and future X-ray and MeV polarimeters such as eXTP,
COSI, and AMEGO-X, have good chances to detect hadronic polarization during
flares. However, the hadronic polarization cannot be well constrained during
the quiescent state. Nonetheless, if some blazar jets possess relatively stable
large-scale magnetic structures, as suggested by radio observations, a
non-trivial polarization degree may show up for the hadronic model after a very
long exposure time ($\gtrsim 1$ year).
