Can a Distance Derived from Redshift be Seen as a “True” Distance if we Consider a Distant Galaxy to be Stationary Relative to the Milky Way galaxy? [closed]

The expression $$d=zc/H$$ is a nonrelativistic approximation, valid in the limit that $z\ll 1$ and correspondingly the recession speed $Hd\simeq zc\ll c$. In this low-velocity regime, relativistic effects like Lorentz contraction and the relativity of simultaneity are negligible, so there is no ambiguity about the distance.

For a FLRW cosmology (that is, a homogeneous universe) with Hubble rate $H(z)$, The full expression is $$d=c\int_0^z \frac{\mathrm{d}z'}{H(z')}.$$ Assuming that the observed object is comoving with the Hubble flow, $d$ is the distance to that object's worldline measured along the comoving synchronous spatial surface, which is the 3D surface (in 4D spacetime) on which all observers who are comoving with the Hubble flow agree on the time elapsed since the beginning of the universe. In particular, all observers agree on the definition of these surfaces, so all observers agree on the distance $d$.

Let's be clear. $cz/H_0$ is a distance measure, but it cannot be considered any kind of absolute or "true distance", and nobody involved in cosmology thinks it is.

If by "true distance" you mean the proper distance - the distance to a galaxy that it has at the current cosmic epoch, that would be measured if you could somehow lay a long line of metre rulers together, then that is given by $$ d_{\rm true} = c \int_0^z \frac{dz'}{H(z')} \ , $$ where $H(z)$ is the Hubble parameter as a function of redshift and I am assuming the galaxy moves in concert with the cosmic expansion. $H(z)$ depends on the model for the cosmological expansion and hence on the model parameters (e.g., $\Omega_M, \Omega_\Lambda$ in the $\Lambda$CDM model).

Hubble's law in its purest form does also give $d_{\rm true}$, but only when the current Hubble parameter $H_0$ is multiplied by the rate of change of proper distance, which is only approximated to by $cz$ at small redshifts.

Since the universe is assumed homogeneous and isotropic on large scales in the usual expansion models, then it makes no difference at all if we consider things "from the other galaxy's point of view" (i.e. an observer at that galaxy considers it is stationary and that the Milky Way is moving away), as long as we are considering the the same cosmic epoch. i.e. At the same cosmic epoch, an observer in the other galaxy would measure the redshift of the Milky Way to be approximately$^*$ the same as we measure the redshift of that other galaxy, and would estimate the same proper distance to the Milky Way since their measured values for the cosmological parameters should also be the same.

$^*$ There could be small effects associated with the position of the observer within the galaxy - gravitational redshift and rotation.

Edit: The redshifts being discussed in this question that are those associated with universal expansion, and inserted into the equation above or Hubble's law, are not arbitrary. They are defined with respect to the comoving frame that is at rest with respect to the locally measured cosmic microwave background (CMB). Both the emitting galaxy and the observer need to be at rest in this frame for the equation above to apply. Since they are not in general (the Earth moves at $\sim 370$ km/s with respect to the CMB), then measured Doppler shifts have to be corrected for this in order to use them as "redshifts" in cosmological formulae and distance estimation. That correction also needs to be applied for the emitting galaxy, but its peculiar velocity with respect to to the CMB would usually be unknown. This introduces an additional uncertainty into distance estimates using redshifts, though one can reasonably assume the average peculiar velocity is zero and that peculiar velocities are of order 100-1000 km/s - an uncertainty that becomes negligible compared with the cosmological redshift beyond 100 Mpc.

The reason for this discussion is to explain that you are not free to apply arbitrary velocity shifts to the frame of reference of the emitting galaxy or observer and then use Hubble's law or the equation above. If you choose alternative frames of reference you will get different distances. The only agreed upon distance, that might be regarded as the "true distance", is that defined above for the proper distance, where the redshift used assumes the emitter and observer are locally at rest with respect to the CMB.

In your edit where you clarified the meaning of "true distance" as being the actual distance right now, you have missed out on one of the important features of special relativity: there is no such thing as "right now" which extends beyond a single event $E$ of space-time.

There is such a thing as the "future" of $E$: it consists of all space-time events $F$ which can be reached by inertial motion starting at $E$ with some initial (sub-light) velocity. And there is a "future light cone" of $E$, consisting of all space-time events $F$ which can be reached by the motion of some photon that starts at $E$ and heads off with some initial direction. If you reverse those, you get the "past" of $E$ and the "past light cone" of $E$.

But that leaves out a whole swathe of space-time that is completely inaccessible to $E$, namely the exterior of the total light cone of $E$.

Suppose we consider any two space-time events $F_1$ and $F_2$ in the exterior of the total light cone of $E$. Perhaps $F_2$ is in the future light cone of $F_1$, or perhaps the other way around, or perhaps neither. However, you and I, sitting together at the space time event $E$, in the late evening, each with a cup of rapidly cooling tea, and gazing up together at some momentary flash in the sky, have no way to reach any kind of conclusion of the form "$F_1$ is happening now but $F_2$ is not happening now".

Yes, I can imagine a shortest possible ruler extending from $E$ to $F_1$ and of some total length (sadly, I cannot measure that length, and in fact no such ruler exists in physical reality; but at least it exists in an abstract mathematical sense). And I can imagine another such ruler for $F_2$. But even those two rulers extend out into the exterior of the light cone of $E$. In particular, I cannot say that one of those rulers is in some kind of extended "now" simultaneous with $E$, whereas the other ruler is not.