What is the ruling on checking classmates' academic results without their permission, when these results are available on a public website on Google?

The default rule is that academic grades are private to the student, and it is not permissible to view or publish them without their permission, because they might be low, and the student would dislike people seeing them. It is permissible to view them if the student gives permission for that, or if they publish them themselves in a public place.