Judge yourself, not others, according to 9 spiritual traditions

Ere thou canst settle in Jñâna Mârga and call it thine, thy Soul has to become as the ripe mango fruit: as soft and sweet as its bright golden pulp for others’ woes, as hard as that fruit’s stone for thine own throes and sorrows, O Conqueror of Weal and Woe. (Blavatsky, The Voice of the Silence, 3, 261)

 Perhaps one of Carl Jung's more useful contributions to psychology was his elaboration of the notion of projection, something that the ancients seemed to be aware of, as the following quotes would suggest, and so modern psychology brings new insight into an age-old problem and supports the validity of ancient ethics:

Buddhism

One should pay no heed to the faults of others, what they have done and not done. Rather should one consider the things that one has oneself done and not done. (Dhammapada, 4, 50)

Reveal your own shortcomings,/but do not seek out others' errors./ Conceal your own good qualities,/but proclaim those of others.  (Atisa, Bodhisattva's Jewel Garland 3, (Jinpa 25))

If you lapse and find yourself noticing another’s shortcomings, think ,’This is my own deluded perception; no such flaw exists in them. All sentient beings are endowed with the essence that shares the Buddha’s own nature.’ Reflect in this manner and judge this perception to be your own flaw. (Se Chilbu Chokyi Gyaltsen, "A Commentary on the 'Seven-Point Mind Training'", 6.3 (Jinpa 97))

Hinduism

Non-calumny: When one sees somebody drowning, he does not bother whether that person is a brahmin or an untouchable, but thinks that saving him is his first duty. Such a person, instead of bothering about the failings of another, tries to overcome that by his own good qualities and does not taunt him about them. Not taunting people for their failings by comparing them with perfect persons is the indication of non-calumny and there is no doubt that this is one of the resting stages in the path to liberation. (Dnyaneshwari; 16:68-212, transl. M.R. Yardi) 

Taoism

People through finding something beautiful
Think something else unbeautiful,
Through finding one man fit
Judge another unfit. (Lao Tzu, Tao Te Ching, 2)

He who knows others is learned; he who knows himself is wise. (Lao Tzu, Tao Te Ching, 33)

Confucianism

Zigong was criticizing other people. The Master said: "Zigong must have already reached perfection, which affords him a leisure I do not possess." (Confucius, Analects, 14,29)

Judaism

Do not taunt your neighbour with the blemish you yourself have. (Babylonian Talmud. pp. Baba Metsiya 59b, Kiddushin 70a)

If one judges his fellow favorably positively, he will be judged favorably by the Omnipresent. (Talmud, Shabbat 127b)

Christianity

1 Judge not, that ye be not judged.
2 For with what judgment ye judge, ye shall be judged: and with what measure ye mete, it shall be measured to you again.
3 And why beholdest thou the mote that is in thy brother's eye, but considerest not the beam that is in thine own eye?
4 Or how wilt thou say to thy brother, Let me pull out the mote out of thine eye; and, behold, a beam is in thine own eye?
5 Thou hypocrite, first cast out the beam out of thine own eye; and then shalt thou see clearly to cast out the mote out of thy brother's eye.  (Matthew 7:1–5)

Stoicism

Let philosophy scrape off your own faults, rather than be a way to rail against the faults of others. (Seneca, Moral Letters, 103.4a-b)

Sufism

Lord, teach me not to judge anyone if I have not walked a day or two in their sandals. Lord, teach me to withhold my tongue in criticizing someone if I have not walked a day’s journey with him. (Yunus Emre, Yunus Emre Hazretleri Sohbet ve Nasihat, Mehmet Fayzi [Conversations with and Advices of Hazrat Yunus Emre], p.19)

Let not the pious judge the meek
Each for his own deeds will speak.
Whether I’m good or bad, you judge yourself;
You reap what you sow, find what you seek.

(Hafiz Shirazi, Ghazal 80, Shahriar Shahriari)

Sikhism

O Nanak, if someone judges himself, only then is he known as a real judge (Gurbani, SGGS 148).

ਨਾਨਕ ਪਰਖੇ ਆਪ ਕਉ ਤਾ ਪਾਰਖੁ ਜਾਣੁ ॥: Nanak parkhe aap kayu ta paarakh jaan

Let each person examine his own mind, O brother (Gurbani, SGGS 1128).

ਇਸੁ ਮਨ ਕਉ ਕੋਈ ਖੋਜਹੁ ਭਾਈ ॥ Is mann kayu koee khojo bhaaee

Theosophy

It (theosophy) has to find objective expression in an all-embracing code of life thoroughly impregnated with its spirit -- the spirit of mutual tolerance, charity and love. Its followers have to set the example of a firmly outlined and as firmly applied morality before they get the right to point out, even in a spirit of kindness, the absence of a like ethic Unity and singleness of purpose in other associations and individuals.

As said before -- no Theosophist should blame a brother whether within or outside of the association, throw slur upon his actions or denounce him {….} lest he should himself lose the right of being considered a theosophist. Ever turn away your gaze from the imperfections of your neighbour and centre rather your attention upon your own shortcomings in order to correct them and become wiser . . . Show not the disparity between claim and action in another man but -- whether he be brother or neighbour -- rather help him in his arduous walk in life . . .

Do not indulge in unbrotherly comparisons between the task accomplished by yourself and the work left undone by your neighbour or brother, in the field of Theosophy, as none is held to weed out a larger plot of ground than his strength and capacity will permit him . . . Do not be too severe on the merits or demerits of one who seeks admission among your ranks, as the truth about the actual state of the inner man can only be known to, and dealt with justly by KARMA alone. Even the simple presence amidst you of a well-intentioned and sympathising individual may help you magnetically . . . You are the Free-workers on the Domain of Truth, and as such, must leave no obstructions on the paths leading to it.

(Some Words on Daily Life, The Original Programme of the Theosophical Society, Ostende, October 3, 1886, Blavatsky, Collected Writings 7, 173-7)