Is it permissible to work as a data monitor on social media sites, given that the job requires looking at obscene and pornographic posts to ensure that the site's policies are not violated?

The default ruling is that it is permissible to work in censorship, provided that its laws and regulations do not contradict Islamic law. The work is not forbidden merely because it sometimes necessitates viewing impermissible scenes. Indeed, it was permissible to look at what is uncovered of women for the purpose of establishing a hadd (prescribed punishment) or giving testimony, and it was permissible to listen out of necessity for inquiry, such as a ruler listening to people of discord, and to look at non-mahram women out of need. However, one must limit one's gaze to the extent of the need, lower one's gaze from impermissible scenes, and strive to prevent their appearance.