Praise be to Allah.
What your parents have asked you to do of teaching this imam does not come under the heading of cooperating in sin and transgression. The fact that this imam goes against sharee’ah in some issues means that you have to advise him and remind him lest he continue with those infractions and fall into others, especially as you are going to form a special relationship with him by teaching him English.
Cooperating in sin and transgression would be the case if you were to be the cause of some sin or continuing it or spreading it, or if you helped the one who is doing it with some idea or money or physical help.
Examples of cooperating in sin and transgression include: renting out stores to riba-based banks or stores that sell haraam things, joining a businessman in manufacturing, selling or buying haraam things, or helping followers of bid’ah (innovation) financially or by enabling them to speak to the Muslims, and so on.
In the verse (interpretation of the meaning): “Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression” [al-Maa’idah 5;2], Allaah enjoins His believing slaves to help one another to do good deeds, which is righteousness, and to avoid bad deeds, which refers to piety; and He forbids them to help one another in falsehood or cooperate in sin and haraam actions.
Tafseer Ibn Katheer (1/12, 13)
Because this imam has some good qualities, we hope that you can strengthen them and help him to fulfil them and attain more. This will be cooperating in righteousness and piety. As for his bad qualities, we hope that you will denounce them and advise him to give them up, and this will also come under the heading of cooperating in righteousness and piety and the sincere advice that is required of Muslims.
It should be noted that the fear about this imam being influenced by staying in the land of kufr does not apply only to him, rather it applies to him, to you and to all the Muslims. What we have seen and heard is sufficient proof that people are influenced.
We have previously stated that it is not permissible to stay in a kaafir country unless one has a legitimate shar’i excuse and meets the conditions laid down by sharee’ah. This has been explained in the answers to questions no. 12866, 6154 and 13363.
And Allaah is the Source of help.