No. At the moment, Christians are to judge those in the church (1 Cor. 5:12; cf. 1 Cor. 6:5) and, in the future, they will ‘judge the world’ (1 Cor. 6:2) and even “judge angels” (1 Cor. 6:3). But, for the time being, Christians are not to judge those outside the church: they are to leave that to God. As Paul says:
…what have I to do with judging outsiders? Is it not those inside the church whom you are to judge? God judges those outside…. [1 Cor. 5:12-13]
Of course, the most important “judging” we are to do is of ourselves because, ‘if we judged ourselves truly, we would not be judged’ (1 Cor. 11:31).