What is the ruling on earning a living from programming mobile applications that display advertisements containing Shariah-prohibited content, despite the programmer exerting every effort to filter these advertisements, but they may not be entirely free of some of them?

Earning profit from advertisements is permissible if the advertisements are permissible. As for impermissible advertisements, it is not permissible to profit from them. If you are in need of this work and have exerted effort to prevent impermissible advertisements, and some still remain, then you must identify the impermissible portion and dispose of it by spending it on charitable causes and public welfare.