Ascertaining the position
In order to answer the question in the node heading -- How can a thinking, rational adult be an atheist? -- we need to ascertain the atheist position. Among other things the atheist position is negative, i.e. the atheist denies the existence of supernatural Beings. We might also observe that in our particular (European, American, Oceanian) cultures this denial concerns most often a single supernatural Being, i.e. it’s mainly a denial of the Monotheist Hypothesis.
Hence the Atheist Hypothesis ("there exists NO supernatural Being, who controls …" etc.) can be succinctly formulated as:
(1) There exists no X who is Y
Digressing and comparing
Digressing for a moment, let us compare this clever statement with the Monotheist Hypothesis ("there exists an Almighty Creator, who is …", etc.). The Monotheist Hypothesis can be given equally succinctly, like in the following lapidary version:
(2) There exists X who is Y
This –- the Monotheist Hypothesis –- is clearly a non-contradictory statement. So in this particular sense it is logically correct. At the same time it can be easily seen that it is totally devoid of any empirical information. As long as we are not presented with a method for empirically identifying X and Y, then we are not given any information about anything factual. So the statement may be perfectly logically correct (non-contradictory), but we can unfortunately not draw any practical conclusions from it.
In both the Monotheist and the Atheist Hypotheses above the somewhat anthropocentric pronoun "who" is used, darkly implying that the X is some individual and hence in some sense a human-like Entity. Here this is merely done to follow established tradition –- Deities are traditionally seen as human-like, both by their defenders and their attackers. But the "who" could of course just as well be replaced by the biologically neutral pronoun "that", without losing any structural clarity.
Existing and non-existing invisible green horses
Is there any difference, regarding their logical non-contradictory status, between statements (1) and (2)? No, of course not. Both are saying something about undefined abstract entities. There is nothing contradictory in the way that this is said in either one of the statements. If I say "There is an invisible green horse who is devilishly clever", then this statement is no less contradictory than saying "There is NO invisible green horse who is devilishly clever".
Hence the Atheist Hypothesis is logically "correct", just as the Monotheist Hypothesis is correct. But by the same token, the Atheist Hypothesis is quite as devoid of any empirical information as the Monotheist hypothesis. So we can not draw any practical, moral or ethical conclusions from the Atheist Hypothesis, like we could not draw any practical or moral conclusions from the Monotheist Hypothesis.
No, not a thinking, rational adult
Would a thinking, rational adult base his or her world-view on something that was devoid of informational content, and hence utter nonsense? No, I should think not.
There is a minor caveat, though. The argument above concerns the fiery crusading atheist, the person who preaches from a soap-box on Hyde Park Corner and elsewhere, pestering us all. Such a person may not be an altogether thinking, rational adult.
However, there are many people who are able to identify simple statements that are empty of empirical information. Such people may exhibit total indifference to them, understandably so.
If such a disinterest in simplistic constructs like "There exists X who is Y" is interpreted as "atheism", then it is of course possible to be a rational, thinking adult and at the same time be an "atheist".