We are a group of young emigrants in Germany. Allaah The Almighty has guided us to adhere to the rules of Islam and to call the German people to embrace it. We have formed a committee in our mosque to assume this task. Now, we have regular activities such as introducing Islam to Germans in the streets, organizing lectures on Islam, and arranging visits to the mosque. We have also launched our own website.
We have noticed that women are greatly interested in visiting the mosque. A brother has criticized us for allowing women to enter the mosque without wearing Hijaab. Moreover, some brothers consider it unacceptable to allow non-Muslims into the mosque. What are the regulations that should be observed in this case?
Has it been authenticated that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, allowed the disbelievers to enter his mosque for the purpose of calling them to Islam?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

May Allaah The Almighty  bless you and your efforts in the field of Da'wah (Islamic propagation).  Please refer to Fatwa 4041 for the ruling on allowing disbelievers to enter the mosque. The summary of that Fatwa is that it is permissible to allow non-Muslims to enter any mosque - except for the Holy Mosque in Makkah - if there is a need for this, such as calling them to Islam. 

However, when calling women to Islam, you should be very careful because women are one of the many trials for men.  Therefore, when you speak to them, only speak about matters related to Da'wah. Also, you must not gaze at them and you should avoid being alone with a woman in a private place. It is recommended that if a man does call women to embrace Islam, he should be accompanied by his wife or any of his Mahram (unmarriageable kin) women.  If this is not possible, a man should not sit with a woman in a place with a closed door, because when a man and woman are alone, they are in the situation where Satan would tempt them to sin. The Prophet, sallallaahu ‘alayhi wa sallam, stated this in a Hadeeth narrated on the authority of Ibn ‘Umar .  [Ahmad and At-Tirmithi]

 If all these regulations are observed, there is no reason not to call women to Islam. However, do not forget that your sincere adherence to Islamic teachings is the most effective way to call people to Islam.

Allaah Knows best.