Wa `alaykum as-salamu wa rahmatullah wa barakatuh
In the Name of Allah, the All-Merciful, the Mercy-Giving
All praise is due to Allah. Peace and blessings be upon him His Messenger Muhammad.
Authentic hadiths tell us that the Messenger of Allah received non-Muslim individuals and delegations in his mosque. He even tied a non-Muslim captive, named Thumamah ibn Uthal, to one of the pillars of his mosque, to let him watch Muslims performing their prayers; and finally the man accepted Islam.
Therefore, it is permissible for non-Muslims to enter mosques and Muslims should seize such opportunities to introduce Islam to them in the best way. But it is noteworthy in this context that such non-Muslims have to show respect to the mosque and to Muslims in terms of their clothes and conduct inside the mosque.
It is only prohibited for them to enter the Sacred Mosque in Mecca as mentioned in Surat al-Tawbah, verse 28.
Almighty Allah knows best.
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