Praise be to Allaah.
There is nothing wrong with non-Muslims entering the mosque if it is for a legitimate shar’i purpose or for a permissible reason, such as listening to lessons or drinking water, etc., because the Prophet (peace and blessings of Allaah be upon him) let some of the non-Muslim delegations stay in his mosque, so that they could see the people praying and listen to his recitation of Qur’aan and his sermons, and so that they could call them to Allaah from close at hand. And the Prophet (peace and blessings of Allaah be upon him) tied up Thumaamah ibn Athaal al-Hanafi in the mosque when he was brought to him as a prisoner of war, and Allaah guided him and he became a Muslim. And Allaah is the Source of strength.
From Majmoo’ Fataawa wa Maqaalaat Mutanawwi’ah li Samaahat al-Shaykh al-‘Allaamah ‘Abd al-‘Azeez ibn ‘Abd-Allaah ibn Baaz (may Allaah have mercy on him), vol. 8, p.356
But with regard to groups of tourists entering mosques just to look around, accompanied by woman who are improperly dressed and carrying cameras, who enter mosques without respect, this is a great wrong which should not be allowed. And Allaah is the One Whose help we seek.
Sheikh Muhammed Salih Al-Munajjid