Cosmology must have issues with evidence.
Once an object is beyond our solar system, it is impossible to send a probe there for a direct measurement.
The only available data from a distant object are its spectrum.
Spectrum analysis of absorption and emission lines has a long history of experiments. There is no reason to doubt them.
We can take the spectrum of a narrow slice of a spiral galaxy disk.The observation reveals blue shifted hydrogen emission lines on one side but red shifted on the other side. This is consistent with the expected disk rotation.
When a proton captures an electron, the new hydrogen atom emits this wave length. With the proton in motion, the line is shifted. It is either red or blue depending on its direction at that instant.
A quasar has an active plasmoid. It is attracting anything with a positive charge. Metallic ions are moving toward it. As each captures an electron, each emits that emission line for that state change.
High velocity protons also move toward this plasmoid. When it captures an electron, it emits the hydrogen emission line just like in a spiral galaxy. For the quasar, positive charges move only toward the plasmoid so all emission lines sr red shifted.
M31 spectrum has calcium ions with a blue shift. They are moving away from the M31 galactic corona at the same velocity calcium ions move away fron our Sun. These ions are absorbing energy from M31, not capturing electrons, so the calcium ion absorption line is measured. It is blue shifted because the ions are moving away from M31 or toward us.
A moving heat source is known to affect the remote temperature measurement. The Doppler effect on the heat source results in the spectrum shift observed as a temperature change.
The Sun is known to wobble around the barycenter. An exoplanet search technique is known as the wobble method or the radial velocity method.
The calculated orbits for the explanets are Keplerian ellipses.
In each case the Doppler effect is confirmed as consistent.
However, beyond our Local Group aninconsistency arises.
There is a hydrogen absorption line with a cumulative red shift. Depending on the IGM in the line of sight this red shift seems to be roughly proportional to distance.
We have never sampled the IGM so it is impossible to experiment with its behaviors. The observational evidence indicates this cumulative red shift.
Therefore only the IGM is unique. In all other cases the atomic blue or red shift indicates the atom's velocity.
The problem in cosmology is none of these atoms in motion are relevant to the galaxy or quasar.
The problem is not with the Doppler effect behaving in some convoluted manner, like a cosmological red shift, which violates thermodynamics.
Cosmologists make the mistake of believing with no justification the galaxy or quasar is moving at the velocity of an atom.
The evidence is for a consistent Doppler effect. The evidence is also for a consistent mistake trying to use it with distant objects.