Shaking hands with non-mahram women or men is not permissible, and if you explain this to them to make them familiar with the Islamic culture, they will normally understand you. Attending a gathering in which an unlawful act is being committed is not permissible. Working for non-Muslims is not haram on the condition that the job is lawful, decent and allowable, not resulting in Muslims' contempt or humiliation. Watching non-Muslim women with no hijab or watching their picture is permissible only on the condition that there is no intention of seeking pleasure, and the pictures do not show nude or half-naked women. The obligatory precaution demands that disbelievers be prevented from entering the mosques and the holy shrines of the infallible Imams, peace be upon them. Unless they want to do research on Islam, or giving them the permission to do so leads to their optimism about Islam and makes them interested in Islam and Muslims. However, they should take religious observances in to consideration so as to not make the mosque impure.