I do not understand the math, but as I understand, yes this is an unresolved problem of cosmology. The Wikipedia article on the "cosmological principle" starts like this:
Unsolved problem in physics: Is the universe homogeneous and isotropic at large enough scales, as claimed by the cosmological principle and assumed by all models that use the Friedmann–Lemaître–Robertson–Walker metric, including the current version of the ΛCDM model, or is the universe inhomogeneous or anisotropic?
It is all very well covered on Wikipedia. Here are some selective quotes from the same article:
Karl Popler wrote: the “cosmological principles” were, I fear, dogmas that should not have been proposed.
Although the universe is inhomogeneous at smaller scales, according to the ΛCDM model it ought to be isotropic and statistically homogeneous on scales larger than 250 million light years. However, recent findings have suggested that violations of the cosmological principle exist in the universe and thus have called the ΛCDM model into question, with some authors suggesting that the cosmological principle is now obsolete and the Friedmann–Lemaître–Robertson–Walker metric breaks down in the late universe.
European Space Agency says:
Planck's new image of the CMB suggests that some aspects of the standard model of cosmology may need a rethink, raising the possibility that the fabric of the cosmos, on the largest scales of the observable Universe, might be more complex than we think.
To sum up:
"Why do we still believe that the universe is isotropic then?"
I do not know. Probably because it is the best explanatory model we have. More data supports it than not.
As to the more general question: why do people believe the things they do? I do not think physics can explain that. Try metaphysics and/or philosophy :)