As the author of that linked answer, I'll first say that I agree with @Yishai that Rav Shternbuch's position is not at all as clear as I made it out to be. In truth, Rav Shternbuch is not interested in answering any questions regarding what non-Jews should or should not do; he is merely responding to questions that Jews have regarding their non-Jewish neighbors or employees. HE even discourages his Jewish correspondent from having anything to do with attempting to draw non-Jews into adhering to their commandments, beyond "influencing them to live lives of justice and uprightness." (Having said that, I should note that other rabbinic authorities - perhaps most notably the Lubavitcher Rebbe, Rav Menachem Mendel Schneerson - would likely disagree with Rav Shternbuch on this point).
Now, to the text of Rav Shternbuch. In Teshuvos Vehanhagos 3: 264, he writes regarding forcing gentiles living in the land of Israel to become 'geirei toshav (towards the bottom of page 290):
דבגר תושב אין החיוב רק לשמור השבע מצוות לבד ככל בן נח, שהרי הוא צריך גם להאמין בהקב"ה, ומה עוד שהוא צוה לעשותן, וע"ז אין כופין שלא שייך כפייה להאמין, ורק על מה שלא מקיים ז' מצוות מצינו דחיוב מיתה.
regarding a ger toshav, the obligation is not merely to observe the seven commandments like all Sons of Noah - for he must also believe in God, and that He commanded that [these laws] be observed. On that, [the Jews] cannot force [the non-Jews], because you cannot force a belief
Rav Shternbuch goes on to discuss for several paragraphs how the concept of ger toshav is a voluntary acceptance, which the responsibility of the Jewish people in their land cannot extend to forcing a belief system. From these pages, it is hard to tell whether or not Rav Shternbuch would say that a non-Jew is actually permitted to be an atheist, or if he is only saying that Jews should not bother themselves with attempting to influence their beliefs.
However, later in Teshuvos Vehanhagos 3:317, it appears to me that Rav Shternbuch clarifies that the Noahide is under no obligation to believe whatsoever:
כשכופין אותו לקבל אין זה קבלה כלל... וכ"ש לפי המבואר אצלינו במק"א שבן נח אמנם מצווה שלא לעבוד ע"ז אבל אין בז' מצוות אזהרה להאמין רק לא לעבוד ע"ז, ובנעשה גר תושב נשתנה דינו שמקבל ע"ע בזה האמונה
if we [Jews] were to force [the gentile] to accept, this is not an 'acceptance' at all... and all the more so according to what we have explained elsewhere, that although Sons of Noah are commanded not to serve idols, they is no commandment among the seven commandments a requirement [literally, 'warning'] to believe; only not to serve idols, and when he becomes a ger toshav his status changes for he accepts upon himself this belief
To me (although I see how others might read it differently), this paragraph indicates that Rav Shternbuch felt that there are two reasons why a Jew should not bother to influence gentiles' beliefs: (1) because a coerced belief is not a belief at all, and (2) anyways, non-Jews are not commanded to believe in God, merely prohibited from idolatry. His reasoning seems to be simply that there are 'seven commandments', not more, and belief in God is not one of them. It is perhaps worth noting that Rav Shternbuch does refer in this piece to gentiles who hold heretical beliefs, and warns Jews to distance themselves from such heretics even more than they must distance themselves from idolatry - but does not say anything about whether or not this is permitted for those gentiles.
