Is working in Android app programming, which relies on ad revenue, permissible, given that there are filters to prevent forbidden ads such as alcohol and sex, but there is no 100% guarantee that these filters will be applied, and ads featuring immodestly dressed women or interest-based banks may appear? And is the necessity of work a justification for that?

There is no objection to working in the field of programming and uploading applications to Google Play, provided that ads are filtered to prevent impermissible content. The appearance of immodest images in some permissible ads does not affect this, because it is a widespread affliction and difficult to guard against, and these images are not the intended subject of the advertisement. As for browsing ads and earning from them, there is no objection if they are permissible and free from deception and trickery, such as giving advertisers the impression that a large number of people have viewed them when the reality is otherwise.