How well they fit the data. All the data. Which includes a lot more than red shifts.
As a very easy example we've already covered at length, none of your ideas have ever fit the CMB at all.
Objectively, the standard model doesn't fit all the evidence either.
The CMB was predicted to be a consequence of an expanding universe.
Besides the original prediction, is there any other piece of evidence that ties the CMB to an expanding universe?
If one made a theory that tied an earthquake in Turkey 120 years ago to the US economy in the 1980's, it would probably be the best the theory there is that fits both pieces of evidence.
But what if the two pieces of data aren't related? That means the best theory for the data, is still a bad theory.
So, has there ever been any independent confirmation that the CMB is related to the redshifts?
Were LCDM to have successfully predicted the expansion rate we measure, I suppose that would count. But obviously, it isn't successful. That's just one of its significant flaws:
Eight Significant Shortcomings of the Standard Model of Cosmology
Problem 1: The observed spectral amplitude of the CMB is below the predicted value
Problem 2: No satisfactory explanation of the quantum-to-classical transition between inflation and the hot Big Bang
Problem 3: Why is the Higgs vacuum expectation value the same everywhere?
Problem 4: Lithium fails to match the predictions of Big Bang nucleosynthesis
Problem 5: The low-entropy configuration as required by ΛCDM is extremely unlikely
Problem 6: Observations show fully-formed galaxies while ΛCDM predicts stars only for the same epoch
Problem 7: Discrepancy between independent measurements of the Hubble constant
Problem 8: ΛCDM is inconsistent with Einstein’s equivalence principle
https://new-ground.com/en/articles/...dard-model-of-cosmology/new-ground.2023.77033
Problem's 1, 5, and 7 due to the CMB.
The CMB also has three significant anomalies: a cold spot, asymmetric hemisphere temperatures, and the correlation with our solar system, aka, axis of evil.
This list doesn't include the
S8 tension, also due to the CMB data.
How can we be sure the microwave radiation in question is even cosmological in nature?
It's original predicted temperature isn't right, it's the source of several major "cracks" in the standard model of cosmology, and it contains anomalies.
At what point do we permit some skepticism as to origin?