All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
In case the nature of work in these institutions is based on Calling to Allah, then there are necessarily two points to be considered:
First, if the person makes this Calling to Allah for the sake of getting a worldly benefit, not for the reward in the Hereafter, then it is considered a work not for the Sake of Allah. Regarding it, Allah, The Exalted, says (what means): {Whoever desires the life of this world and its adornments - We fully repay them for their deeds therein, and they therein will not be deprived.} [Quran 11:15] There would be no reward for the doer of this act.
Second, if the intention is to get closer to Allah and meanwhile to earn a worldly benefit, then this is a permissible act – a fact recorded in the Saying of Allah, the Exalted (which means): {There is no blame upon you for seeking bounty from your Lord.} [Quran 2:198] This verse was sent down concerning the ritual of Hajj. According to an authentic Hadith of the Prophet “Ukadh, Mijannah and Dhul-Majaz were markets during the pre-Islamic period. The Companions disliked trading there till the following verses of the Noble Qur'an were revealed: “There is no sin on you if you seek the Bounty of your Lord (during Hajj)…”
However, one should do his best to make sincerity to Allah the guide to all his deeds and actions and to place the worldly benefit second in rank.
Truly, whoever sincerely works for the sake of Allah, He, the Exalted, would facilitate for him all affairs – as Allah, The Exalted, says (what means): {Obedience and good words. And when the matter [of fighting] was determined, if they had been true to Allah, it would have been better for them.} [Quran 47:21]
Allah knows best.