The adjective censorious means someone who often criticizes other people.
Synonyms are accusatory, critical, complaining, or condemning.
The word origins from Latin (1530s) censorius meaning “pertaining to a censor”, also “rigid, severe”. It also comes from censor meaning “magistrate” plus –ious.
The students feel awkward in a solemn and censorious class setting.
Molly rolled her eyes at the censorious tone of his voice.
The senator has a censorious attitude to those who don’t share the same opinion as his.