Is it biblical for someone to be put out of the church?

Yes. It certainly is. The failure of many churches to exercise this biblical practice is one reason many are in such a sorry state. It is never something to be taken lightly and is of course open to abuse. But, simply ignoring open sin in the church is definitely unbiblical as is ignoring false doctrine.

1 Corinthians 5 contains both a specific example as well as the rationale for putting a person out of church. Basically if uncorrected the 'bad leaven' will have an effect on the whole church. This is precisely what happens and is happening in churches today which ignore this. Saying 'you shouldn't judge' sounds pious but is a misuse and a mis-understanding of what the Bible teaches, including Jesus Himself. The passage in Corinthians clearly teaches that Christians are to judge other Christians or people who claim to be so. They are of course to be loving and kind to those who are not. The context here is the Christian church.

The passage below specifically deals with immoral behaviour. Other passages deal with the importance of pure doctrine. So it is quite biblical and the Bible also sets out the right way to do it, humility being the first requirement.

1 Corinthians 5:1-13 1It is reported commonly that there is fornication among you, and such fornication as is not so much as named among the Gentiles, that one should have his father's wife.

2And ye are puffed up, and have not rather mourned, that he that hath done this deed might be taken away from among you. 3F

or I verily, as absent in body, but present in spirit, have judged already, as though I were present, concerning him that hath so done this deed,

4In the name of our Lord Jesus Christ, when ye are gathered together, and my spirit, with the power of our Lord Jesus Christ,

5To deliver such an one unto Satan for the destruction of the flesh, that the spirit may be saved in the day of the Lord Jesus.

6Your glorying is not good. Know ye not that a little leaven leaveneth the whole lump?

7Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even Christ our passover is sacrificed for us:

8Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened bread of sincerity and truth.

9I wrote unto you in an epistle not to company with fornicators:

10Yet not altogether with the fornicators of this world, or with the covetous, or extortioners, or with idolaters; for then must ye needs go out of the world.

11But now I have written unto you not to keep company, if any man that is called a brother be a fornicator, or covetous, or an idolator, or a railer, or a drunkard, or an extortioner; with such an one no not to eat.

12For what have I to do to judge them also that are without? do not ye judge them that are within? 13But them that are without God judgeth. Therefore put away from among yourselves that wicked person.