First of all, it is noteworthy that Islam encourages tolerance and peaceful co-existence between Muslims and non-Muslims. If non-Muslims enter a mosque to deliver speeches that may lead to a better understanding, then it is welcomed and religiously recommended. Islam is the religion of constructive dialogue in the fullest sense. The history of Muslims is a very good example of this.
Dr. Muzammil Siddiqi, former president of the Islamic Society of North America (ISNa) and member of the Fiqh Council of North America, states that: “It is good to invite non-Muslims to visit the masjid and see the Islamic way of Prayer, but they should be told beforehand about the Islamic rules of dress and modesty especially in our place of worship. If they are informed beforehand with courtesy and kindness, they will understand and appreciate the rules. It is seen that most of them observe these rules very carefully. However, if there are some visitors who are not properly dressed, you may give them something clean to cover themselves before they enter the masjid, or you may overlook this negligence in the broader and more important interest of giving the message of Islam to them.
In Islam there is something called Fiqh Al-‘Awlawiyyat, or understanding priorities. We should keep in our mind the rules of priorities. The common sense rule is that when you are confronted with two evils, you may accept the lesser evil in order to fend off the major one and achieve greater good. So in this case you are faced with a choice, either you turn away a non-Muslim from your place of worship and let that person not know about Islam and have a bad impression of Islam and Muslims, or you allow her to come, even without proper dress, and then learn about Islam and possibly become a Muslim. If this is the choice then it is better to accept the person without proper dress and treat her well. Hopefully she will learn some good things about Islam and Allah may guide her to the right path.”