All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
It is permissible for a Muslim to work for non-Muslim relief organizations if they do not have forbidden activities – such as calling to Christianity and the like – because in principle it is permissible for a Muslim to hire himself out to a non-Muslim as long as his work does not involve doing what is forbidden or helping in it. Ibn Qudaamah said in al-Mughni – about a Muslim hiring himself out to a Thimmi:
“If a Muslim is hired for doing a particular job for a Thimmi (non-Muslim living in the Muslim community) like sewing a dress or shortening it, then this is permissible without any difference of opinion that we know of, because ‘Ali hired himself out to a Jewish man as a laborer to draw water from a well in return for a date per bucket (to irrigate the Jewish man’s orchard). The Prophet was informed of that and did not object to it. The same thing happened with an Ansaari man; that is because it is a contract by which the worker gets a recompense (for his job), and it does not involve humiliating the Muslim or using him for one’s own personal needs, and this is similar to buying and selling with him [the non-Muslim]. Also, if he hires himself out to him for a job other than serving (offering mean services to) him, for a known period, it is permissible, according to the apparent meaning of the words of Imaam Ahmad, as he said in the narration by al-Athram, if he was to do a given work, it is permissible, and Ahmad ibn Sa’eed, reported from him, 'It is permissible for him to hire himself out to a Thimmi, and this is general in regard to hiring jobs.'”
For more benefit, please refer to fatwas 250321 and 17051.
Moreover, the Kuwaiti Fiqh Encyclopedia reads:
“Muslim jurists agreed that it is allowable for a Muslim to hire himself out to a non-Muslim to do a specific, well-defined job, such as tailoring a garment, building a house, cultivating land, and the like. This is because ‘Ali hired himself out to a Jewish man as a laborer to draw water from the well in return for a date per bucket (to irrigate the Jewish man’s orchard). The Prophet was informed of that and did not object. Another reason for making it permissible is that the Muslim worker who hires himself out to do a specific job may get someone else (a third party) to do that specific job for which he was hired. Muslim jurists also agreed that it is impermissible for a Muslim to hire himself out to a disbeliever to carry out forbidden tasks such as wine-making, shepherding pigs, and the like.”
Allaah Knows best.