Islam does not prohibit anyone from visiting a mosque as it is a House of God, open to people of all faiths, and those of none at all. According to Islam, non-Muslims are even allowed into the Sacred Mosque in Mecca and Medinah.
Once, a delegation of Christians from the Arab city of Najran came to meet the Holy Prophet Muhammad (peace be upon him) in Madinah. After some time, the Christians became restless and so the Holy Prophet (peace be upon him) enquired if something was wrong. In response, the Christians informed him that it was time for their worship, but they did not have an appropriate place to perform their prayers or rituals. Upon this, the Prophet of Islam (peace be upon him) invited the Christians to worship in his own mosque in Madinah, according to their traditions and ways. (Ibn Hisham, I, 575-577)