Giving Tochacha - even if it causes embarrassment and degradation - for bein Adam L'Makom mitzvos

update Rabbi Shain has additional sources that he asked to be posted

http://yudelstake.blogspot.com/2014/08/rambam.html

BM (59a): Better it is for man to cohabit with a doubtful married woman1 rather than that he should publicly shame his neighbour. Whence do we know this? — From what Raba expounded, viz., What is meant by the verse, But in mine adversity they rejoiced and gathered themselves together... they did tear me, and ceased not?2 David exclaimed before the Holy One, blessed be He, ‘Sovereign of the Universe! Thou knowest full well that had they torn my flesh, my blood would not have poured forth to the earth.3 Moreover, when they are engaged in studying "Leprosies" and "Tents"4 they jeer at me, saying, "David! what is the death penalty of him who seduces a married woman?" I reply to them, "He is executed by strangulation, yet has he a portion in the world to come. But he who publicly puts his neighbour to shame has no portion in the world to come."’5

       Mar Zutra b. Tobiah said in Rab's name — others state, R. Hana6 b. Bizna said in the name of R. Simeon the pious — others again state, R. Johanan said on the authority of R. Simeon b. Yohai: Better had a man throw himself into a fiery furnace than publicly put his neighbour to shame. Whence do we know it? — From Tamar.7 For it is written, when she was brought forth, she sent to her father-in-law [etc].8

 Berachos(19b):     R. Judah said in the name of Rab: If one finds mixed kinds3 in his garment, he takes it off even in the street. What is the reason? [It says]: There is no wisdom nor understanding nor counsel against the Lord;4 wherever a profanation of God's name is involved no respect is paid to a teacher.

Rambam(Hilchos De'os 6:7-8): 

Halacha 7

It is a mitzvah for a person who sees that his fellow Jew has sinned or is following an improper path [to attempt] to correct his behavior and to inform him that he is causing himself a loss by his evil deeds as [Leviticus 19:17] states: "You shall surely admonish your colleague."

A person who rebukes a colleague - whether because of a [wrong committed] against him or because of a matter between his colleague and God - should rebuke him privately. He should speak to him patiently and gently, informing him that he is only making these statements for his colleague's own welfare, to allow him to merit the life of the world to come.

If he accepts [the rebuke], it is good; if not, he should rebuke him a second and third time. Indeed, one is obligated to rebuke a colleague who does wrong until the latter strikes him and tells him: "I will not listen."

Whoever has the possibility of rebuking [sinners] and fails to do so is considered responsible for that sin, for he had the opportunity to rebuke the [sinners].

Halacha 8

At first, a person who admonishes a colleague should not speak to him harshly until he becomes embarrassed as [Leviticus 19:17] states: "[You should]... not bear a sin because of him." This is what our Sages said: Should you rebuke him to the point that his face changes [color]? The Torah states: "[You should]... not bear a sin because of him."

From this, [we learn that] it is forbidden for a person to embarrass a [fellow] Jew. How much more so [is it forbidden to embarrass him] in public. Even though a person who embarrasses a colleague is not [liable for] lashes on account of him, it is a great sin. Our Sages said: "A person who embarrasses a colleague in public does not have a share in the world to come."

Therefore, a person should be careful not to embarrass a colleague - whether of great or lesser stature - in public, and not to call him a name which embarrasses him or to relate a matter that brings him shame in his presence. 

When does the above apply? In regard to matters between one man and another. However, in regard to spiritual matters, if [a transgressor] does not repent [after being admonished] in private, he may be put to shame in public and his sin may be publicized. He may be subjected to abuse, scorn, and curses until he repents, as was the practice of all the prophets of Israel.

Rav Elchonon Wasserman (Kovetz Ha’aros #70):...It would seem that all that is prohibited between people (bein adam l’chavero) is only prohibited when done in a harmful and destructive manner without justification. For example regarding the prohibition of “Not hating your brother.” This is only prohibited for gratuitous hatred (sinas chinom). In other words when he is not doing anything wrong (davar ervah). However if he is doing something wrong then it is permitted to hate him. It is important to note that the reason for hatred being permitted in this case is not because of the fact that a sinful person is not considered your “brother.” Tosfos (Pesachim 113b) explains that if you hate this sinful person for another reason then you transgress the prohibition. The hatred is only permitted because of the bad (davar ervah) that you see in him. Similarly regarding the prohibition of beating another, the Rambam writes that it is prohibited only if done as fighting (derech netzoyan). This is clear from the fact that it is permitted for a teacher to his student. And this that we noted before in Sanhedrin (84b) – that is only a rabbinic restriction. And similarly concerning the prohibition of causing anguish to a widow or orphan, Rambam (Hilchos De’os 6:10) writes that if it is done to teach Torah or a trade – there is no prohibition. Similarly concerning the prohibition of lashon harah, it is permitted against people who cause discord and quarrels in order to stop the fight. Similar concerning using words to cause anguish (onas devarim), it is permitted publicly criticize someone publicly if it is for the sake of chastisement. It is even permitted to publicly embarrass someone if it is done for the necessity of chastisement for a person who has not stopped his bad behavior after being rebuked in private. In such a case it is even permissible to curse him. In fact this is what was done by the prophets in the past as the Rambam (Hilchos De’os 6:8) notes. We thus shown from all this, that all the prohibition involving interpersonal actions do not apply when the act is beneficial.