Is it permissible to work in programming applications for institutions that have both permissible and forbidden activities at the same time, knowing that the program itself does not contain any content that violates Islamic law? And is one absolved of responsibility for the program's use in forbidden acts if there was no intention to assist in such acts?

If the primary purpose of the program is permissible, and the impermissible aspect is minor and incidental, there is no harm in providing it to the beneficiary, because what is incidentally overlooked is not intentionally overlooked. Also, the prevalence of such violations has become widespread, provided that the individual does not directly engage in the impermissible act or command it. As for selling the program, one must investigate and verify the condition of the beneficiary. If it is known that the primary purpose is impermissible use, then providing the program is forbidden. However, doubt does not necessitate prohibition, and it is permissible to stipulate non-use for impermissible purposes as a precautionary measure.