If you think the author is wrong about their pet theory of general relativity, why do you think they're right in their disproof of LCDM?

I don't know whether his theory is wrong. In the end I'm not qualified to make that claim.

Despite all the crackpottery of the auther ("'dark' age", "Einsteins blunder"...) there are some things that he does different than other crackpots. He doesn't resort to interpreting the words instead of the math of physics nor does he avoid to make testable predictions nor does he cherry-pick or creatively reinterpret data. For the SDSS data less so than serious astro physicists apparently.

His curves which quite well fit the raw SDSS data seem to be derived from an unusual but 'simple' spacetime geometry and are not notably fitted to parameters - quite opposite to the LCDM curves which he took from standard sources (those only fit comparatively cherry picked galaxies). Thus judging from raw SDSS data LCDM could be considered severely challenged.

He also gives all the sources he uses, the SDSS queries used in the graph generation, how the magnitudes are calculated, how the results apply in different spectral lines. All relevant considerations you'd rather expect in serious work. It is only tained by his extraordinary claims, his ego and other crackpottery traits (like making grande generalizations about everyhing).

The link you posted reeks strongly of crackpot,

Totally. That's why I added the disclaimer. I edited it a bit to make that more clear. The author matches all criteria for crackpot no doubt. But even a crackpot can stumble upon something.

I do not have credentials in astronomy. I'm somewhat well-read in the subject and can handle sufficient math. And when checking the presented data (I did actual SDSS queries; the SDSS explorer and query facilities are genuinely cool) it appears that there is something to his claims - if not to his theory itself.