Here's a prediction of the FLRW theory.

If I stand on any planet $P$ anywhere in the universe, and look at any galaxy $G$ from the point of view of planet $P$, and compute the distance $D$ between $P$ and $G$, and compute the red-shift $R$ of $G$ from the point of view of $P$, the value of $R$ depends on $D$ alone. This prediction is testable (albeit with difficulty, given that no human being has ever yet been to another planet).

What prediction does the "anthropocentric theory" make regarding the appearance of red shifts on planet $P$? Does it make any prediction at all? If not, that's a definite flaw in the theory.

Here's a prediction of the FLRW theory.

If I stand on any planet $P$ anywhere in the universe, and look at any (sufficiently far) galaxy $G$ from the point of view of planet $P$, and compute the distance $D$ between $P$ and $G$, and compute the red-shift $R$ of $G$ from the point of view of $P$, the value of $R$ depends on $D$ alone. This prediction is testable (albeit with difficulty, given that no human being has ever yet been to another planet).

What prediction does the "anthropocentric theory" make regarding the appearance of red shifts on planet $P$? Does it make any prediction at all? If not, that's a definite flaw in the theory.