Is it permissible to work as a public relations manager for a company that displays immodest images and immoral websites, given that they also have religious channels and that your work involves translating their religious content?

It is permissible to work in companies that have mixed fields (forbidden and permissible), provided that the questioner's work is in the permissible field, such as translating religious topics or other permissible tasks. This is evidenced by the Prophet's (peace be upon him) and Ali ibn Abi Talib's dealings with the Jews, despite their knowledge of the Jews' usurious transactions. This indicates the permissibility of dealing with a transgressor and an owner of mixed wealth if the transaction is in a permissible matter.