Is it permissible for a Sunni to marry a Shiite?

If not, how can we bring them closer to Sunni?

Well, it may need different approach individually. We need to explain them what Islam is. The main issues that they have in term of aqeedah that the attributes that they give to their Imaams and their worship of their Imaams. If you are a Sufi, who was already worshiping the saints, and you marry the shiite, it is a marriage among one of a kind. You are no different from shiite.

But if you are Sunni, meaning that you are following Qur’an and Sunnah, and you worship only Allah, you should not marry a shiite. It is the same case when you marry a Sufi – you are calling others besides Allah.