Is it permissible to work as a data entry clerk for an establishment that sells clothes featuring images and some nudity, knowing that this is disapproved of and advice has been given to avoid it, but to no avail?

It is permissible to work in entities whose primary activity is lawful, even if they present some prohibited activities, provided that the employee does not directly engage in the prohibited work himself.

This is detailed as follows: - If the primary activity of the company is prohibited, such as usurious banks, then working there is absolutely forbidden. - If the primary activity of the company is lawful, but it engages in some prohibited activities, then working there is permissible under the following conditions: - The product must not be specifically intended for a prohibited matter, or predominantly used for it. - The employee must not directly engage in the prohibited work himself.

Therefore, there is no objection to working in this institution as long as the employee does not directly engage in matters related to selling prohibited items.