MISCONCEPTION 1: Muslims Worship the Pagan Moon god

Moon gods

Points: 

• A lot of Muslim countries have the moon and star on their flags.
• Muslims use the moon to tell when a new month arrives, like when to begin fasting.
• Muslims pray according to the position of the moon and sun.
• Muslims use 'ALLAH' just like the pagan Arabs.

REFUTATION: 

• The use on the moon and star on the flags of a lot of Muslim nations started with the coming of the Ottoman empire as a unifying symbol and to acknowledge the fact that these bodies are creations of ALLAH. The Prophet (SAW) himself never used them on any flag but all the same, the intention with which an action is done determines the stand of Muslims on it. Using the moon and star (as a symbol alone) constitutes no harm in Islam. Going deeper, it is greatly prohibited to worship anything as a means of worshiping ALLAH as this is clearly declared ‘Shirk’ (associating partners with ALLAH). ALLAH tells us in Suratul Fussilat (41:37) “Do not prostrate to the Sun or to the Moon but prostrate to ALLAH who created them if you really worship HIM” 
• Secondly, it was not a strange thing to use the position or size on the moon and star to calculate dates. It simply shows that even without the time telling technologies around today; the Muslims were self-sufficient when came to keeping up with time. ALLAH (SWT) tells us: "It is He Who made the Sun to be a shining glory and the Moon to be a light (of beauty), and measured out stages for her; that you might know the number of years and the count (of time). Nowise did Allah create this but in truth and righteousness. (Thus) does He explain His Signs in detail, for those who understand. Suratul Yunus (10:5) ALLAH (SWT) says in another verse: "They ask thee concerning the New Moons. Say: They are but signs to mark fixed periods of time in (the affairs of) men, and for Pilgrimage". Suratul Baqarah (2:187). From these verses, we see that it is ALLAH HIMSELF commanding Muslims to utilize these bodies, we therefore do so to obey ALLAH (SWT) and not to worship them. As regards fasting, the Prophet (SAW) commanded us thus: “Do not fast until you see the Crescent and do not break the fast until you see it. Estimate about it in case it is cloudy.” (Al-Bukhari 1773). Hence, we as people who strive to follow the instructions of our Prophet to the most minute detail use the moon to determine when to fast. 
• Muslims observe five daily prayers spread across each day, accuracy of time and unity is essential here therefore, ALLAH (SWT) gives us an easy means of achieving this. "Establish prayer at the decline of the sun [from its meridian] until the darkness of the night and [also] the Qur'an of dawn. Indeed, the recitation of dawn is ever witnessed". Suratul Isra’ (17:78). Again, it is ALLAH's command.
• People from virtually all tribes of the world had terms with which they referred to beings they felt were divine and supreme and most times, even when the deity changed; the name remained the same. Take for instance the Hausa tribe in West Africa, their ancestors were definitely pagans worshipping one carved or molded object or the other. At any particular time, they referred to their most supreme being as ‘ubangiji’. Today, over 90% of ethnic Hausas are Muslims and they still used the term ‘Ubangiji’ on some occasions to refer to their God which is now ALLAH (SWT) mentioned in the Qur’an. The point here is-the deity changed, the intension changed, the concept changed, the set of beliefs changed but the name remained. Today, if you remind a Hausa man of what his ancestors worshipped as ‘ubangiji’; he would weep for them because he now belongs to a faith that rightly sees those set of belief as null en void. The word al-Lat was used as a name and title for multiple pre-Islamic goddesses of Arabia and was used for either a wife of Allah or a daughter depending on the region. ALLAH (SWT) tells us in the Glorious Qur’an:

Say, "He is Allah , [who is] One,

Allah , the Eternal Refuge.

He neither begets nor is born,

Nor is there to Him any equivalent." Suratul Ikhlas (112)

From this chapter of the Qur’an we see that the concept of ALLAH of the pre-Islamic is not identical to that of the Muslims. The ‘allah’ of the pre-Islamic Arabs had wives, children brothers and so on, but the ALLAH of Muslims is in no need of such. In the conquest of Macca, the Prophet (SAW) showed no tolerance for the deities of the Maccans; the idols representing their own version of ALLAH were all crushed leaving only the concept of the Muslims standing. The shrine and temple dedicated to al-Lat in Taif was demolished on the orders of Muhammad (SAW) during the Expedition of Abu Sufyan ibn Harb in the same year as the Battle of Tabuk. The destruction of the idol was a demand by Muhammad (SAW) before he would allow any reconciliation to take place with the tribes of Taif. In the Qur’an, ALLAH goes on to declare the deities of the pre-Islamic Arabs absolutely nothing to look up to.

So have you considered al-Lat and al-'Uzza?

And Manat, the third - the other one?

Is the male for you and for Him the female?

That, then, is an unjust division.

They are not but [mere] names you have named them - you and your forefathers - for which Allah has sent down no authority. They follow not except assumption and what [their] souls desire, and there has already come to them from their Lord guidance.

Suratul Najm (53:19-23)

Conclusively, the ALLAH of the Qur'an is pure and divine with no blemishes and that is the BEING that Muslims worship.