  Matter at ultra-high densities finds a physical realization inside neutron
stars. One key property is their maximum mass, which has far-reaching
implications for astrophysics and the equation of state of ultra dense matter.
In this work, we employ Bayesian analysis to scrutinize the mass distribution
and maximum mass threshold of galactic neutron stars. We compare two distinct
models to assess the impact of assuming a uniform distribution for the most
important quantity, the cosine of orbital inclination angles ($i$), which has
been a common practice in previous analyses. This prevailing assumption yields
a maximum mass of $2.25$~$M_\odot$ (2.15--3.32~$M_\odot$ within $90\%$
confidence), with a strong peak around the maximum value. However, in the
second model, which indirectly includes observational constraints of $i$, the
analysis supports a mass limit of $2.56^{+0.87}_{-0.58}~M_\odot$ ($2\sigma$
uncertainty), a result that points in the same direction as some recent results
gathered from gravitational wave observations, although their statistics are
still limited. This work stresses the importance of an accurate treatment of
orbital inclination angles, and contributes to the ongoing debate about the
maximum neutron star mass, further emphasizing the critical role of
uncertainties in the individual neutron star mass determinations.
