A very serious problem here is that atheists are using two contradictory definitions of Nature and Naturalism at the same time. One definition of Nature is the universe, which is fine. The other definition of Nature is a universe which is purely physical and therefore is not rational and has no purpose. This second definition predetermines the argument without viewing the evidence, which is what atheists are trying to do. The second definition completely distorts our understand of reality by taking rationality, meaning, and purpose out of life and the universe. This is what @GJDS was referring to as the creed/world view of New Atheism.
Now to say that the universe is structured in a way to allow for the creation of life is a truism. Whether this proves God is another question. However it does seem to me that the evolution of life on earth does indicate that Nature is rationally structured, because evolution favored the creation of humans who are rational.
It is not that other creatures are irrational, but humans are have taken rationality to a different level which gives them control over themselves and their environment. This situation where humans are raised to a level higher than the rest of nature, indicates that there must be a God over humans and the rest of nature or that humans alone are metaphysical, which we know is not true.
Carroll tries to attack fine-tuning by completely separating Nature (which can be done only by using the second false definition of Nature) from God, which is not true. When one begins with a false assumption, one comes to a false conclusion.