What is the ruling on eating, drinking, and dealing with innovators at work? Is it permissible to believe someone among them who swears falsely? And how can they be convinced of the rulings of Islam?

The food of the people of innovation (Ahl al-Bid'ah) is permissible, but if their innovation is one that entails disbelief (kufr), then it is not permissible to eat their slaughtered animals.

Shaykh Ibn ‘Uthaymeen said: "The innovation of the people of innovation should be examined; if their innovation entails disbelief, then it is not permissible to eat their slaughtered animals… But if the innovation does not entail disbelief, then there is no harm in eating their slaughtered animals."

As for believing their reports, one should be cautious of them and verify their news, because they consider lying and dissimulation (taqiyyah) as part of their religion, in accordance with the Almighty’s saying: "O you who have believed, if there comes to you a disobedient one with information, investigate, lest you harm a people out of ignorance and become, over what you have done, regretful." (Al-Hujurat: 6).

As for inviting them [to the truth], those who are academically qualified should undertake this, and it should be done with wisdom and good admonition, by clarifying the truth, establishing the evidence, and removing misconceptions.