Question: Was there any specific criteria for the differentiation between autonomous republics of the Russian SSR (like Tatarstan) and for the USSR republics properly (like Kazakhstan)?

That is, why did some of the ethnic minorities of the Russian Empire just got to be autonomous republics within Russia and not direct Soviet republics?

Not at all. I'm an atheist, but saying that CE is "more correct" is silly.

It tries to cut ties with religious connotations but it still has Jesus's alleged birth as basis, so....

Not to mention that even the days of the week in most European languages (English included) have religious-related names (though not Christian). I'm not seeing anyone arguing that we should change the name of the 5th (or 4th, depending on the convention used) day of the week (thursday) just because Thor is no longer worshipped.