Is one allowed to sit next to a person who has a cross on their necklace or a lucky charm or a chain with a blue eye in it if we do not know if the person wears it for protection or because of another reason?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

It is not prohibited for the Muslim to sit next to someone wearing a prohibited item such as a cross, an amulet, or the like. This may happen in public places, like means of transportation, and prohibiting it would involve putting people in difficulty and hardship. Hence, it is not prohibited to sit next to him, but if you can give them advice with wisdom and knowledge, you should hasten to do so, following the example of the Prophet, sallallahu ‘alayhi wa sallam. ʻImraan ibn Husayn, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, saw a man wearing a brass ring (bangle) on his upper arm. He exclaimed, "Woe to you! What is this?" The man replied, "This is to protect me from weakness in the hand." The Prophet, sallallahu ‘alayhi wa sallam, said, "Verily, it will only increase your weakness. Cast it away from you, for if you die with it on you, you will never be successful." [Ahmad, Ibn Maajah, At-Tabaraani, Al-Haakim in Al-Mustadrak] Some Hadeeth scholars declared the hadeeth's chain of narration to be authentic, and others classified it as weak.

It is deduced from the hadeeth that the Muslim should inquire about the reason for wearing the prohibited item first and then forbid the person from wearing it in a wise manner.

Allah knows best.