If an astrophysical jet contains gamma rays does it mean that at the source poles there is small gravitational redshift? If an astrophysical jet contains gamma rays does it mean that even though the source has incredibly strong gravitational pull, at the source poles there is small gravitational redshift? Maybe there is no much gravity if there is a so small grav. redshift?
 A: Let's consider a gamma ray emitted from the surface of a $1.4$ solar mass neutron star, assuming the radius is 10 km (on the low end of what is consistent with observations from LIGO and NICER). Let's also assume the spin is small in units of the mass of the object, (a) for simplicity and (b) consistent with observations of known neutron stars.
The redshift of a light ray emitted from the surface of a (non-spinning) neutron star obeys
\begin{equation}
1+z = \left(1-\frac{R_s}{R_{\rm NS}}\right)^{-1/2}
\end{equation}
where $R_{\rm NS}=10{\ \rm km}$ is the radius of the neutron star, and
\begin{equation}
R_s = \frac{2GM}{c^2} = 4.1\ {\rm km}
\end{equation}
is the Schwarzschild radius of a $1.4$ solar mass object.
Plugging in the numbers we find that $z=0.3$. In other words, if the energy of the emitted gamma ray was $100\ {\rm keV}$ (a typical scale associated with the gamma rays observed from 170817, a collision of two neutron stars), then the energy of the gamma ray that is observed far away from the neutron star is $100{\ \rm keV}/(1.3)=77\ {\rm keV}$. So, there is some effect from gravitational redshift, but it is not enough to make a qualitative difference. (note that the exact boundaries between what is called a gamma ray, vs an X-ray, are somewhat fuzzy, and in astronomy what typically matters more is the process producing the radiation more than the radiation itself)
Said differently, neutron stars are compact objects, but not so compact that their gravitational field is enough to strip the majority of the energy from emitted radiation.
