Does Islam allow us to judge others?

It is often said "Don't judge me!" by Muslims. In Islam we are all required to judge everyone and everything around us. If we see something wrong, we are required to speak out against it and try to change it. You can't do that without judging. Islam also requires us to reject the testimony of someone who commits open sin, which also cannot be done without judging people. So, Islam requires us to judge people around us, and when someone is an open fasiq - such as not wearing hijab, or not praying salat, or having photos of them free-mixing or at parties with alcohol, etc - then we judge them based on what is outward and call them out for it, especially if they choose to speak from their ignorance and comment about the Deen. Narrated Umar bin Al-Khattab: "People were (sometimes) judged by the revealing of a Divine Inspiration during the lifetime of Allah's Apostle but now there is no longer any more (new revelation). Now we judge you by the deeds you practice publicly, so we will trust and favor the one who does good deeds in front of us, and we will not call him to account about what he is really doing in secret, for Allah will judge him for that; but we will not trust or believe the one who presents to us with an evil deed even if he claims that his intentions were good." (Bukhari 2641)