The standard cosmological model seems to be inconsistent with SR, yet it is generally "believed" that the big bang model is consistent with observations and that it is a pretty good theory.
Personally I think the big bang model leads to complete nonsense, and I can think of possible ways to explain why the universe appears to be expanding without resorting to such crazy ideas.
When rational thinking leads us to irrational solutions we should suspect that we have taken a wrong turn.