Is it permissible to rely on the fatwa from al-Fatawa al-Hindiyyah which states that a garment is not rendered impure if a wet impurity passes over it and the garment does not become wet to the point of dripping, in order to pray in outdoor clothes that may have come into contact with sewage water?

The fundamental principle concerning things is purity. So, unless you are certain that the water has become impure, act according to this principle. If you are certain of its impurity, then the fundamental principle is that it has not affected your garment, unless you are certain that it has. And if you are certain that the garment has been affected by impure water, then there is hope for forgiveness for minor impurities. Some scholars have gone so far as to pardon all minor impurities. The Shafi'is have explicitly stated that minor amounts of impure street mud that splashes onto the clothes of passersby are excused due to the hardship involved.