How should a Muslim man make Da'wah to non-Muslim women?
Praise be to Allaah.
You have to call whoever you can to Islam and to enter the religion of Allaah. You have to show them the strengths and distinctive features of this great religion and explain to them how suited it is to mankind. You have to tell them that it offers brilliant solutions to human problems and tell them, that they have to follow this religion and no other. All of this should be done on the basis of sound knowledge, evidence and proofs of which you have a firm and proper knowledge, and it should be done with wisdom and beautiful preaching, responding to the kaafirs with that which is better.
The way you make dawah and your manners should be in accordance with the rulings of Islamic shareeah, so it is not permissible for example for you to be alone with a kaafir woman, not even for the sake of Dawah. You must beware of forming relationships with women, and you should be aware of the ways in which the Shaytaan introduces evil, whereby you efforts to make dawah and draw closer to Allaah by offering advice to kaafir women may end up with you being tested and tempted by them. Dawah to non-Muslim women should either be undertaken by Muslim women, or else by a Muslim man giving them tapes and booklets, or by giving public speeches and lectures without deliberately looking at the women. We ask Allaah to help you in your Dawah and to make your responses correct. May Allaah bless our Prophet Muhammad.