Asalaamu alaykum, and thank you for this question.
I am sorry to hear that this is what your imam is teaching his congregants, as it is not founded in Islam. The truth is that helping anyone, in any circumstance, is a highly rewarded and blessed task.
Muslims today are working hard to help people all over the world. IMAN, the Inner-city Muslim Action Network, is an organization in the poorest parts of Chicago serving the poverty-stricken people there. Most of them are non-Muslim!
The Prophet (peace and blessings of Allah be upon him) said,
I and an orphan’s guardian, whether he is a relative or a non-relative, will be like these two in the Garden,’ and then the transmitter indicated the index and middle fingers. [Sahih Muslim]
On first glance, this may not seem to directly address your question, but think about it: he is saying that he is very very near to someone who works to put the affairs of an orphan in order, whether that orphan is a relative or not.
What Prophet Muhammad is saying here can be extrapolated to anyone who works to help in the affairs of any oppressed or suffering person, whether they are related or not.
Now, imagine what it means to God if we help those who are not even Muslim? Imagine what sort of amazing message we are sending to the world when we help people out of the love of humanity?
It’s not a totally radical idea that good people would help anyone suffering, in any condition.
In another hadith, Prophet Muhammad said:
… Whosoever removes a worldly grief from a believer, Allah will remove from him one of the griefs of the Day of Judgment. Whosoever alleviates [the lot of] a needy person, Allah will alleviate [his lot] in this world and the next. (an-Nawawi)
While he does specifically mention removing suffering from a fellow Muslim here, he goes on to refer to “a needy person”, giving one the impression that it is a great reward to help anyone.
Now, the idea that we should begin our charity with our own family is founded on a sound hadith. The Prophet (peace & blessings of Allah be upon him) said,
The best charity is that which is practiced by a wealthy person. And start giving first to your dependents. [Sahih Al-Bukhari]
So while we should certainly start by helping out the weaker members of our family, beyond that, we are called to help remove the suffering of any human being, Muslim or not.
I hope this answers your question, inshaallah.
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