Matthew 7:1 Judge not, that ye be not judged.

Do not judge lest you be judged is not referring to you correcting anyone. It is referring to you seeing someone who do not know GOD, without telling them about GOD you have concluded they cannot be saved. You have judged them even before their time. Correct them first.

When you are called to come over and settle any misunderstanding, do not go there to find the guilty or innocent one. Rather appease both sides thoroughly with all words of love and calmness. Don't point to anyone nor tell them you're guilty without understanding fully well.

Judgments should not be passed on anyone unless in the rightful courts of law. And also at this, the judge must be very much aware he is not being misled by arranged evidences in order to free the guilty and replace the guilty with the innocent due to any power or a kind of bias.

When you are to settle a quarrel between two people, you are not to condemn anyone quickly because of what they say. For there are times that some people, despite being innocent are not good at explaining causes. Then the other who is good at it turns the table to his own favour.

When you are called to see to an occasion between two people, without knowing who is innocent or guilty yet, do not be in a hurry to pass judgment on anyone of them either in their presence or behind them. For looks can be deceiving in most cases.

When anybody reports anyone to you, do not because of what the report is react immediately without hearing the other side of the story. Because most cases, the person who is not innocent may be the first to come to make a report to you so as to free themselves of the charge.

Do not hate anyone because of what they tell you about them. If you do, you have judged them even without knowing if what they tell you is true or false. Do not bear grudges against them nor take them as an enemy because of what you heard about them.

When you begin to spread an unconfirmed rumor of anybody because someone else said that about them, even though you know it may not be true, you have judged the person already. Find out from the person accused first before you condemn the guiltless.

When you happen to see someone in your dream trying to harm you and you managed to wake up, do not conclude it is that person you saw that is behind this attack. For if you do not understand the wiles of the Devil, you will condemn the guiltless.

These to mention but a few.

Therefore, correcting people in order to save their lives, making them realize their faults and mistake is not being judgmental. Because if you see someone about to fall into a pit and you think keeping quite so as not to offend them because they do not know is the nest option, you have judged them that they need to fall into that pit to realize their state.

Correcting someone is not same as judging them.
For the Word of GOD below !says:

2 Timothy 4:1-4 I charge thee therefore before God, and the Lord Jesus Christ, who shall judge the quick and the dead at his appearing and his kingdom;
Preach the word; be instant in season, out of season; reprove, rebuke, exhort with all longsuffering and doctrine.
For the time will come when they will not endure sound doctrine; but after their own lusts shall they heap to themselves teachers, having itching ears;
And they shall turn away their ears from the truth, and shall be turned unto fables.

Are we now to say the above verses are being judgmental?
Be the judge, yourselves.