This questioner from France asks is it permissible for a non-Muslim to enter a masjid and if it’s not permissible what does a Muslim do if he sees a non-Muslim in the masjid?
See video for answer from Shaykh Zaid B. Haadee (rahimahullah)
It is allowed for a disbeliever to enter the masjid for a purpose; either for fixing something inside that is in need of repair, or to hear something from remembrance and admonition and perhaps he will enter into Islaam as a result of this.
So in conclusion, there is no problem with a non-Muslim entering the masjid for a legitimate purpose. Not to commit an offence or cause corruption in the masjid.
As for if he enters to tear apart the masaahif or to damage the masjid then this is not permitted. Even if he was a Muslim this would not be permitted. So how about if he is a non-Muslim?!
So what is required from us is wisdom* in calling the non-muslims (to Islaam), inviting them and using good speech and humility so that they may enter Islaam after coming to know of the excellence of Islaam from the actions of its people.
*Wisdom comprehensively defined by Al-Imaam Ibnul Qayyim (rahimahullah):
“Wisdom is that you do that which is appropriate, in an appropriate manner, at an appropriate time.” (Madaarij As-Saalikeen 2/449)