Changing an evil is something that does concern a Muslim, it is not one of the things that do not concern him

Firstly: 

There is no contradiction between what is proven in
sharee’ah, whether between one aayah and another, between one hadeeth and
another, or between aayahs and ahaadeeth. All of it is Revelation (wahy)
from Allaah. Allaah says (interpretation of the meaning): 

“Had it been from other than Allaah, they would surely,
have found therein many a contradiction”

[al-Nisa’ 4:82] 

If there appears to be a contradiction, that is in our own
minds and because of our misunderstanding, not in the texts themselves.
Hence the scholars took the care to explain the texts in which there may
appear to be a contradiction and to dispel any confusion that may have
arisen in some people’s minds concerning some texts. With regard to the
question, there is no contradiction – praise be to Allaah – between the
words of the Prophet (peace and blessings of Allaah be upon him),
“Whoever among you sees an evil action, let him change it with his hand [by
taking action]; if he cannot, then with his tongue [by speaking out]; and if
he cannot, then with his heart [by hating it and feeling that it is wrong] –
and that is the weakest of faith” (Narrated by Muslim, 49), and his words,
“Part of a person’s being a good Muslim is his leaving alone that which does
not concern him” (narrated by al-Tirmidhi, 2317, classed as saheeh by Ibn
al-Qayyim in al-Jawaab al-Kaafi, p. 112) 

It is not possible under any circumstances that Islam would
oblige the person who sees an evil action to change it, then at the same
time tell him that it is better not to denounce it. 

The circumstances in which the first hadeeth applies are
different from those in which the second hadeeth applies.  

This is similar to what some people understood from the verse
(interpretation of the meaning): 

“O you who believe! Take care of your ownselves. If you
follow the (right) guidance [and enjoin what is right (Islamic Monotheism
and all that Islam orders one to do) and forbid what is wrong (polytheism,
disbelief and all that Islam has forbidden)] no hurt can come to you from
those who are in error”
[al-Maa’idah 5:105] 

But Abu Bakr al-Siddeeq (may Allaah be pleased with him)
guided them to the correct understanding, and the scholars (may Allaah have
mercy on them) explained that. 

It was narrated that Abu Bakr al-Siddeeq (may Allaah be
pleased with him) said: “O people, you recite this verse (interpretation of
the meaning): 

‘O you who believe! Take care of your ownselves. If you
follow the (right) guidance [and enjoin what is right (Islamic Monotheism
and all that Islam orders one to do) and forbid what is wrong (polytheism,
disbelief and all that Islam has forbidden)] no hurt can come to you from
those who are in error’
[al-Maa’idah 5:105] 

I heard the Messenger of Allaah (peace and blessings of
Allaah be upon him) say, ‘When the people see an oppressor but they do not
try to stop him, soon Allaah will cause all of them to suffer punishment
because of him.’”  

(Narrated by al-Tirmidhi, 2168; Abu Dawood, 4338; Ibn Maajah,
4005). 

This hadeeth was classed as saheeh by al-Tirmidhi and Ibn
Hibbaan, 1/540. 

Shaykh al-Islam said concerning what we learn from the verse
“Take care of your ownselves…”: 

“… Enjoining what is good and forbidding what is evil in the
manner prescribed in Islam, based on knowledge, kindness, patience, good
intentions and doing it in the proper manner, is included in the phrase “Take
care of your ownselves…” and in the phrase “If you follow the (right)
guidance”. 

These five things are what may be learned from the aayah, for
the one who is commanded to enjoin what is good and forbid what is evil. 

There is also another meaning which is that a person should
focus on his own interests by seeking knowledge and acting upon it, and not
worry about that which does not concern him, as the Prophet (peace and
blessings of Allaah be upon him) said: “Part of a person’s being a good
Muslim is his leaving alone that which does not concern him.” Especially
being too curious about that of which a person has no need to know about
another person’s religious commitment or worldly affairs, and especially if
he is speaking because of hasad (destructive envy) or competing in
leadership.  

Majmoo’ al-Fataawa, 14/482 

And he (may Allaah have mercy on him) said: 

The believer has to fear Allaah with regard to His slaves and
it is not his responsibility to guide them. This is the meaning of the verse
(interpretation of the meaning): 

‘O you who believe! Take care of your ownselves. If you
follow the (right) guidance [and enjoin what is right (Islamic Monotheism
and all that Islam orders one to do) and forbid what is wrong (polytheism,
disbelief and all that Islam has forbidden)] no hurt can come to you from
those who are in error’
[al-Maa’idah 5:105] 

Calling others to guidance means doing what is obligatory. If
the Muslim does his duty of enjoining what is good and forbidding what is
evil, and does his other duties as well, then the misguidance of those who
have gone astray will not harm him. That may be achieved sometimes by the
heart, sometimes by the tongue and sometimes by the hand. In the case of the
heart, this is obligatory in all circumstances because doing it will not
cause any harm. Whoever does not even do that is not a believer, as the
Prophet (peace and blessings of Allaah be upon him) said, ‘And that is
the weakest of faith.’”  

(Majmoo’ al-Fataawa, 28/126-128) 

So it is known that denouncing evil is one of the things that
concern the Muslim, and he must denounce it as much as he is able and in
accordance with the interests of sharee’ah. That which does not concern him
cannot be something that is waajib (obligatory) or mustahabb (encouraged).  

There follow the comments of the scholars on the
interpretation of the hadeeth, “Part of a person’s being a good Muslim is
his leaving alone that which does not concern him.” 

(a)    
Shaykh al-Islam Ibn Taymiyah
said: 

The Muslim is commanded either to speak good or to keep
silent. If he turns away from the silence that is enjoined upon him and
speaks in a unnecessary manner that is not good, then this is counted
against him. Hence the Prophet (peace and blessings of Allaah be upon
him) said: “Part of a person’s being a good Muslim is his leaving alone that
which does not concern him.” If a person indulges in something that does not
concern him, that detracts from his being a good Muslim. 

Majmoo’ al-Fataawa, 7/49, 50 

(b)   
Ibn al-Qayyim (may Allaah have
mercy on him) said: 

The Prophet (peace and blessings of Allaah be upon him)
summed up all of piety in one sentence, when he said: “Part of a person’s
being a good Muslim is his leaving alone that which does not concern him.”
This includes not speaking about, looking at, listening to, striking a blow,
walking towards or thinking about anything for no purpose, and keeping away
from all outward and inward actions that have to do with things that do not
concern you. This sentence is sufficient concerning piety. 

(c)    
Ibraaheem ibn Adham said:
 

Piety means leaving alone all doubtful things and leaving
alone that which does not concern you means leaving alone all that is
superfluous. 

In al-Tirmidhi there is a marfoo’ report according to which
the Prophet (peace and blessings of Allaah be upon him) said: “O Abu
Hurayrah, be pious and you will be the most devoted of people (to Allaah).”
 

Madaarij al-Saalikeen, 2/21 

(d)   
Ibn Rajab al-Hanbali said: 

This means giving up haraam things, doubtful things, makrooh
things, and excessive permissible things that are unnecessary, because all
of these things do not concern the Muslim if his Islam is perfect and he has
attained the level of ihsaan. The most important aspect of leaving alone
that which does not concern you is guarding your tongue against idle
speech. 

Jaami’ al-‘Uloom wa’l-Hukam,
1/309-310 

(e)    
al-Zarqaani said: 

Some of them said that what comes under the heading of
leaving alone that which does not concern you is learning branches of
knowledge that are not important and ignoring those that are more important,
such as one who neglects to acquire knowledge that is in his own interests
and occupies himself with learning something that does not benefit anyone
else, such as philosophical debate, and says as an excuse, ‘My intention is
to benefit people.’ If he were sincere he would have started by learning the
type of knowledge that would help him to be guided and cleanse himself of
all blameworthy characteristics such as destructive envy (hasad), showing
off, arrogance, self-admiration, rivalry with one’s peers, trying to put
people down and other characteristics and actions that may doom a person to
Hell. 

Ibn ‘Abd al-Barr said: this hadeeth is an example of concise
speech which includes many noble meanings in a few words, and it is one of
the things that were said by no one before him. 

Sharh al-Zarqaani, 4/317 

(f)     
al-Mubaarakfoori said: 

Al-Qaari said – concerning the meaning of leaving alone that
which does not concern him – this means that which is not his business and
which it does not befit him to say, do, look at or think about. And he said:
what is meant by that which does not concern him is that which he has no
need of and is not essential to his spiritual or worldly affairs, and will
not help him to earn the pleasure of his Lord, because he is able to live
without it, and he can put his affairs straight without it. This includes
all superfluous deeds and words. 

Tuhfat al-Ahwadhi, 6/500 

Secondly: 

With regard to what is to be denounced: this includes every
reprehensible action which Islam stated is abhorrent and which leads to bad
consequences for the one who does it, such as zina (adultery), riba (usury,
interest), looking at haraam things, listening to haraam things, shaving the
beard, allowing one’s garment to hang below the ankles, severing the ties of
kinship, introducing innovations into the religion, and so on. 

It is not necessary to be in a position of authority in order
to change evil actions by one’s hand, or to be a scholar in order to change
them by one’s tongue, rather it is sufficient to be able to change them
provided that that does not result in a greater evil than the one that you
are denouncing. It is sufficient for you to know that this is evil according
to sharee’ah, so you denounce it by speaking out. 

With regard to changing evil actions by one’s heart. This
means hating this evil thing in your heart and leaving the place where it is
happening. 

With regard to your question about seeing some evil things
and wondering whether you should denounce the people who are doing them or
inform the authorities, our answer is that it depends on the action in
question and on who is doing it. If you see an evil action on the part of
someone that you cannot leave him and go and tell the authorities about it,
then you have to denounce him straightaway, because it may be too late
otherwise. 

But if the evil action is major and serious, and you cannot
denounce it on your own, then you have to inform the authorities. 

The point is that evil must be removed, whether by your hand
or the hand of someone else. If that is not possible then it must be done by
your tongue (by your speaking out), and you should not worry whether they
listen to you or turn away from you; all you have to do is convey the
message. Allaah may sow the seeds of guidance in the heart of one of them
because of your words, but the Shaytaan may also suggest to you that you
should forget about denouncing them on the basis that they will not listen to you – so beware of that.

 And Allaah knows best.