Is it permissible for a Muslim working in a university's advertising department to write advertisements that promote matters that may contradict Islam, such as celebrating the International Human Rights Day or conferences on women's rights? And is it permissible for him to continue in this job even though most of his other tasks are permissible?

It is permissible to work in this department in principle. If the questioner is asked to publish or write an advertisement that violates the rulings of Islam, he must refrain from doing so while remaining in his job. There is no objection to writing the advertisements mentioned in the question (such as human rights and women's rights), as their general meaning does not violate the rulings of Islam. The decisive factor is the speaker's intention, and Islam was the first to establish human rights and support women.