It is not permissible to work as a content reviewer in the manner described, because it involves watching and listening to objectionable things and not denouncing all of them; rather it involves allowing some of them to be uploaded and seen by viewers. Therefore this reviewer is sinning by listening to and watching these videos, and by leaving some of this objectionable material for the viewers to see. Allah, may He be Exalted, says: {And cooperate in righteousness and piety, but do not cooperate in sin and transgression. And fear Allah; indeed, Allah is severe in punishment} [Al-Ma’idah 5:2] and {And let there be [arising] from you a nation inviting to [all that is] good, enjoining what is right and forbidding what is wrong, and those will be the successful} [Al `Imran 3:104].
And the Prophet (blessings and peace of Allah be upon him) said: “Whoever among you sees an evil action, let him change it with his hand (by taking action); if he cannot, then with his tongue (by speaking out); and if he cannot, then with his heart (by hating it and feeling it is wrong), and that is the weakest of faith.” Narrated by Muslim, 49.
And he (blessings and peace of Allah be upon him) said: “And whoever calls others to misguidance will have a burden of sin like that of those who follow him, without it detracting from their burden in the slightest.”
The fact that the videos will be uploaded for people to watch whether the reviewer likes it or not does not excuse him from the sin of watching the objectionable material or the sin of approving of what he leaves without erasing it.
This young man must fear Allah, may He be Exalted, and gave up this unlawful job, and he should look for permissible work. Whoever gives up something for the sake of Allah, Allah will compensate him with something better than it.
And he should understand that his provision is already decreed, so he should not seek it by unlawful means.
The Prophet (blessings and peace of Allah be upon him) said: “The Pure Spirit [Jibril] inspired in me the fact that no soul will die until it has completed its allotted lifespan and received its provision in full. So fear Allah and be moderate in striving to earn a living, for no one of you should let thinking that his provision is slow in coming prompt him to seek it by disobeying Allah, for what is with Allah, may He be Exalted, can only be attained by obeying Him.” Narrated by Abu Nu`aym in Al-Hilyah; classed as authentic (sahih) by al-Albani in Sahih al-Jami`, no. 2085.
And Allah knows best.