We have to live with non-Muslims for various reasons. Sometimes we eat and drink together. Sometimes we need to drink water in the same glass. The problem is that many people think, non-Muslim's left over water is impure. So it cannot be drunk.
This idea is not correct. A non-Muslim's left over food is not impure in normal conditions. Their remaining water is not impure, except for if there is any specific cause for impurity. There is no difficulty in drinking from the same glass if needed.
In the Qur'an, polytheists are called 'Najis' i.e. impure - because of the impurity of their beliefs. (Tafseer Ibn Kasir, Note on Tafseer of Surah Tawba verse 28)
In fact, it is forbidden to have deep love and relationship with non-Muslims, participate in their festivals, etc. But it is not forbidden to fulfill their rights as neighbours, and if necessary, to deal with them by observing the limits of Shariah.