It is part of etiquette to refrain from asking people about their private affairs

Many people overstep the mark in speaking to others, and they
do not observe any good manners or modesty. The reason for that is ignorance
and a lack of interest in developing a good attitude or good manners. That
includes what many people do of interfering in that which does not concern
them and asking about people’s private affairs. 

It was narrated from Abu Hurayrah (may Allaah be pleased with
him) that the Messenger of Allaah (peace and blessings of Allaah be
upon him) said:  

“Part of a person’s being a good Muslim is leaving alone that
which does not concern him.” Narrated by al-Tirmidhi (2318); classed as
saheeh by al-Albaani. 

Ibn Rajab said in Jaami’ al-‘Uloom  wa’l-Hikam
(1/114-116): 

This hadeeth represents an important principle of etiquette.
Imam Abu ‘Amr ibn al-Salaah narrated that Abu Muhammad ibn Abi Zayd, the
imam of the Maalikis of his time, said: All good manners and etiquette are
based on four ahaadeeth: 

The words of the Prophet (peace and blessings of Allaah
be upon him): “Whoever believes in Allaah and the Last Day, let him speak
good or else keep silent.” 

And the words of the Prophet (peace and blessings of
Allaah be upon him): “Part of a person’s being a good Muslim is leaving
alone that which does not concern him.” 

And the words of the Prophet (peace and blessings of
Allaah be upon him): “Do not get angry.” 

And the words of the Prophet (peace and blessings of
Allaah be upon him): “The believer loves for his brother what he loves for
himself.” 

The meaning of this hadeeth is that part of his being a good
Muslim is that he refrains from doing and saying that which does not concern
him, and he does and says only that which does concern him, i.e., he has
something to do with it. Mostly what is meant by refraining from that which
does not concern him is guarding his tongue against idle talk. 

In al-Musnad (1/201) it is narrated from al-Hasan that
the Prophet (peace and blessings of Allaah be upon him) said: “Part of
a person’s being a good Muslim is talking little about that which does not
concern him.” [al-Arna’oot said: It is hasan because of corroborating
evidence]. 

‘Umar ibn ‘Abd al-‘Azeez (may Allaah have mercy on him) said:
The one who regards his words as being among his deeds speaks little except
about that which concerns him. And it is as he said. Many people do not
regard their words as being among their deeds, so they are careless and do
not watch what they say. But Allaah has stated that there is nothing good in
much of what people talk about amongst themselves. He says (interpretation
of the meaning): 

“There is no good in most of their secret talks save (in)
him who orders Sadaqah (charity in Allaah’s Cause), or Ma‘roof (Islamic
Monotheism and all the good and
righteous deeds which Allaah has ordained), or conciliation between mankind”

[al-Nisa’ 4:114] 

al-Tirmidhi and Ibn Maajah narrated from Umm Habeebah that
the Prophet (peace and blessings of Allaah be upon him) said:  

“Everything that the son of Adam says is counted against him
and not for him, except enjoining what is good and forbidding what is evil,
and remembering Allaah, may He be glorified and exalted. 

[It was classed as da’eef by al-Albaani in Da’eef
al-Tirmidhi]. 

Some people stated in the presence of Sufyaan al-Thawri that
they found this hadeeth strange, and Sufyaan said: Why do you find this
strange? Allaah says (interpretation of the meaning): “There is no good
in most of their secret talks save (in) him who orders Sadaqah (charity in
Allaah’s Cause), or Ma‘roof (Islamic Monotheism and all the
good and righteous deeds which Allaah
has ordained), or conciliation between mankind” [al-Nisa’ 4:114]. 

Al-Tirmidhi narrated that Anas (may Allaah be pleased with
him) said:  

One of the companions of the Prophet (peace and
blessings of Allaah be upon him) died, and a man said: Glad tidings to him
of Paradise. The Messenger of Allaah (peace and blessings of Allaah be
upon him) said “You don’t know; perhaps he spoke of that which did not
concern him, or he was miserly with something that he could do without.”
Classed as saheeh by al-Albaani in al-Silsilah al-Saheehah (3103). 

Reports with similar meanings were narrated via numerous
isnaads from the Prophet (peace and blessings of Allaah be upon him)
and in some of them it says that the man was killed as a martyr. End quote. 

Al-Munaawi said in Fayd al-Qadeer (7/3): 

It is possible that what is meant is asking a man too many
questions about his situation, which includes asking about that which does
not concern one. That also may lead to embarrassment for the one who is
being asked, because he may prefer not to tell him about his situation, and
if he tells him he may feel upset about that, but if he lies to him or tries
to give indirect answers he may still feel upset, and if he ignores his
question that will be bad manners. End quote.

There are reports from some of the salaf which point to this
matter of etiquette: 

‘Amr ibn Qays al-Malaa’i said: 

A man passed by Luqmaan and there were people with him. He
said to him: Aren’t you the slave of such and such a tribe? He said: Yes. He
said: Didn’t you used to farm by Mount So and so? He said: Yes. He said:
Then how have you ended up as I see you? He said: Speaking the truth and
keeping silent for a long time about that which does not concern me. 

Muwarriq al-‘Ijli said:  

It is something that I have been seeking for so many years,
but I was not able to do it, but I will never stop looking for it. They
said: What is it? I said: Refraining from that which does not concern me. 

Both reports were narrated from Ibn Abi’l-Dunya. 

Abu ‘Ubaydah narrated that al-Hasan al-Basri said: One of the
signs of Allaah’s turning away from a man is that he becomes involved in
that which does not concern him, as a sign that Allaah, may He be glorified
and exalted, has left him to his own devices. 

The above shows people how to adopt this important attitude
and etiquette, and how to interact with one another in accordance with the
guidance of the Prophet (peace and blessings of Allaah be upon him) and
the righteous. 

For more information on this sublime etiquette that is
lacking among many people, see the commentary on hadeeth no. 12 in Jaami’
al-‘Uloom by Ibn Rajab al-Hanbali (may Allaah have mercy on him), where
there is a useful discussion under the heading: Mu’allim fi tarbiyat
al-nafs min husni islaam al-mar’i tarkuhu ma la ya’neehi, written by
‘Abd al-Lateef ibn Muhammad al-Hasan, in the al-Bayaan book series published
by al-Muntada al-Islami in London.  

And Allaah knows best.