The Talmud famously says (in a Baraita on Sukkah 29a) that the Jewish people calculate our calendar by the moon (lunar calendar), and the Nations of the World use the sun (solar calendar). How is this understood as far as the Arab/Muslim calendar which is lunar, and likewise the Chinese calendar, which uses the moon? If, however, these peoples are an exception to the rule, why so? (I heard there is a Maharal about this, but I don't know where.)
I have also been bothered by this exact question and I have not found an answer inside. The Maharal does deal with this midrash in Beer HaGolah 6:2, but his focus is more on explaining how eclipses indicate sin, especially given that they are predictable astronomical phenomena. As @Harel13 says above, I'm not particularly troubled by the Islamic calendar per se because it post-dates the Talmud. It may also be partly based on the Jewish calendar. See https://en.wikipedia.org/wiki/Islamic_calendar. (Though probably at least some Arabs were using a lunar or lunisolar calendar beforehand, which presents the same issue. See below.)
But more generally, Chazal were certainly familiar with non-Jewish lunar calendars. Most importantly, the Babylonians used a calendar very similar to the Jews, including the same lunar months and a 19-year Metonic cycle of intercalated months. Hazal were also familiar with Arabs, who are mentioned in many places in the Talmud, though who knows how familiar they were with the Arabic calendar. (There were also other pre-Talmudic cultures the Rabbis were not in contact with that used the lunar calendar, https://en.wikipedia.org/wiki/Lunar_calendar).
My best explanation so far is that Chazal are speaking in generalities and don't mean all goyim. Or "goyim" may be shorthand for Greece and Rome in particular, given that the statement in Sukkah 29a is a Tannaitic Baraita. You could probably come up with a nice drash about the sun and the moon and Jacob and Esau. (Obviously the Tannaim would have been familiar with Arabs and Babylonians, both of whom are mentioned in Tanakh and Tannaitic sources; my point is they wouldn't have been at the front of a Tanna's mind. In the same way, when American rabbis today say "the non-Jews do such" and such they usually don't mean China).
Another puzzle, not mentioned by OP, is that the Jewish calendar is based on the moon and the sun. So why don't solar simanim also affect the Jews? This svara would support the first Baraita that a solar eclipse is bad for the whole world and pose a problem for the second Baraita that says the Sun is a siman for non-Jews specifically.