Mentioning some of the rulings related to the sutrah.

The Shaykh : ...so it is necessary to have a sutrah. When one has a sutrah, important rulings follow. First, if a person passes between the prayer and the place of his prostration, there is no sin on the one praying; rather, the sin is on the one who passed, as we mentioned earlier.
Second: It is permissible for him to push the passerby, even by striking him. A man is praying with a sutrah, and a man comes to pass in front of him, so he pushes him in the best manner. If he does not stop as they say, if he does not stop in the best manner, he pushes him a second time. If he still does not stop, he may strike him, even if he falls on his backside [everyone laughs!]. Yes, that is correct. However, if he is not praying, or if he is praying without a sutrah, it is not permissible for him to do this pushing at all. These are among the rulings of the sutrah.
The final and most important ruling: There is a hadith in Sahih Muslim that Imam Ahmad ibn Hanbal, the Imam of the Sunnah, acted upon. Three things, if they pass in front of the one praying—meaning between him and the place of his prostration—invalidate his prayer: a mature woman, a black dog, and a donkey. This is if he is not praying with a sutrah. If he is in front of a sutrah, it does not harm him if someone passes in front of him.
These are very important matters that people do not care about. We observe, especially in al-Masjid al-Haram and then in al-Masjid al-Nabawi, women passing in front of men, and no one cares! Neither the passerby cares nor the one praying cares, even though the prayer of those who are praying is invalidated. Of course, this is when they are praying the sunnah and voluntary prayers, or perhaps making up what they owe, they claim, and so on. However, if they are praying behind the imam, the imam is a sutrah for those behind him.