Praise be to Allah.
There is no basis in shareeah for taking the crescent or star as a symbol of the Muslims. This was not known at the time of the Prophet (peace and blessings of Allaah be upon him), or at the time of the Khulafa al-Raashidoon (the first four leaders of Islam after the death of the Prophet (peace and blessings of Allaah be upon him), or during the time of the Umawis (Umayyad dynasty). It emerged some time after that, and historians differ as to when this symbol was first adopted and who was the first to adopt it. Some say it was the Persians, others say it was the Greeks, and that this symbol was somehow passed to the Muslims.(See Al-Taraateeb al-Idaariyah by al-Kittaani, 1/320). It was said that the reason why the Muslims adopted the crescent was that when they conquered some western countries, the churches there had crosses on top of them, the Muslims replaced the crosses with these crescents, and the practice spread in this way. Whatever the case, symbols and banners must be in accordance with the teachings of Islam, and as there is no evidence that this symbol is prescribed by Islam, it is better not to use it. Neither the crescent nor the star are symbols of the Muslims, even though some Muslims may use them as symbols.
As regards what Muslims think about the moon and the stars, they believe that they are part of the creation of Allaah, and as such can neither benefit nor harm people, and they do not have any influence over events on earth. Allaah has created them for the benefit of mankind, an example of which is seen in the aayah or verse of the Quraan (interpretation of the meaning):
They ask you (O Muhammad) about the new moons. Say: These are signs to mark fixed periods of time for mankind and for the pilgrimage [al-Baqarah 2:189]
[The commentator] Ibn Katheer said, explaining the phrase Say: these are signs to mark fixed periods of time: From them (the new moons) they may know the times for repaying loans, the iddah (waiting period) of their women [after being divorced or widowed] and the timing of their Hajj (pilgrimage) Allaah has made them signs to mark the times when Muslims should start to fast and break their fast [the beginning and end of Ramadaan], to count the iddah of their women and to know the times for repaying loans.(Tafseer Ibn Katheer).
[Another commentator] Al-Qurtubi (may Allaah have mercy on him) said in his commentary on this aayah [verse]: This explains the wisdom behind the waxing and waning of the moon, which is to avoid any confusion in appointed dates, dealings, oaths, Hajj, iddah, fasting, breaking fasts, length of pregnancy, rentals and other matters that concern mankind. Similar to this aayah are others (interpretation of the meanings):
And We have appointed the night and the day as two aayaat (signs). Then, We have made dark the sign of the night while We have made the sign of day illuminating, that you may seek bounty from your Lord, and that you may know the number of the years and the reckoning [al-Isra 17:12]
It is He Who made the sun a shining thing and the moon as a light and measured out its (their) stages, that you might know the number of years and the reckoning [Yoonus 10:5]
Counting the new moons is easier than counting days.(See Tafseer al-Qurtubi).
With regard to the stars, the scholars of Islam say that Allaah created these stars for three reasons: to adorn the heavens, to drive away the devils (shayaateen) and as signs for navigation.(Saheeh al-Bukhaari, Kitaab Bad al-Khalq), as Allaah says (interpretation of the meaning):
It is He Who has set the stars for you, so that you may guide your course with their help through the darkness of the land and the sea [al-Anaam 6:97]
And indeed We have adorned the nearest heaven with lamps, and We have made such lamps (as) missiles to drive away the shayaateen (devils), and have prepared for them the torment of the blazing Fire. [al-Mulk 67:5]