What is the Biblical basis for the formal 'membership' requirements that some Baptist churches have?

Dr Peter Masters of the Metropolitan Tabernacle Baptist Church, London, has written a booklet entitled "Church Membership in the Bible" which claims "this book answers many questions about churches and church membership in New Testament times." and "..membership of a good church has a powerful formative influence on the believer's life."

I shall mostly quote some of the Bible verses mentioned in the booklet:-

There are a number of Bible verses which presuppose the idea of church membership:

"If a man desire the office of a bishop (or overseer) he desires a good work." (1 Timothy 3:1). Overseer means an inspector, or over-watcher, who has legitimate authority or care over others. The notion of oversight and church government collapses without a membership.

"For if a man know not how to rule his own house, how shall he take care of the church of God?" (1 Timothy 3:5). The local church is like a family, and the responsibilities and duties of a father are very like those of the overseer to the church.

"Let the elders that rule well..." (1 Timothy 5:17). Once again we must ask, how can there be "rule" in a church which has no constituted membership?

1 Corinthians 5 contains much that presupposes a membership. "To put away from among yourselves that wicked person" (v13) means more than just to prevent someone from taking the Lord's Supper. Yet it does not mean prevent them from attending worship, because such worship includes unbelievers: it must mean to put them out of a recognised membership of the local church.

And Matthew 18:15-20 also presupposes a church membership.

It sounds like you think you are going to fail at choosing a church. Like anything, if you think you are going to fail, most likely you are going to fail.

A church is a family. With many problems and differences like any other family.

What was the Church like in the 1st century?
I don't see it any different than today.

1) Jews and Gentiles had their diffences. How to achieve equality, Romans 15:27

They were pleased to do it, and indeed they owe it to them. For if the Gentiles have shared in the Jews’ spiritual blessings, they owe it to the Jews to share with them their material blessings.

2) Divisions in the church. 1 Corinthians 11:18

In the first place, I hear that when you come together as a church, there are divisions among you, and to some extent I believe it.

The church met in houses back then. Can we imagine the level of proselytization between them? Arguing and persuading the people and one another as to what house to go to for communion.

Primary, at Church is where you partake in the Holy Communion. So, one thing to consider when choosing a house church. Proverbs 17:1 NET

Better is a dry crust of bread where there is quietness than a house full of feasting with strife.

However, they were together in one mind. They knew that each house belonged to one church. And the church had the name of the city. The apostles would reference them as a whole. i.e. Church at Jerusalem, Church at Antioch, Church of God, etc.

What does the Bible says about membership between churches?
It doesn't. Not in terms you are talking about in your question. There is only One Church of Christ Jesus.

Who is a member of the church according to the Bible?
Who ever has the seal of the Holy Spirit. Ephesians 1:13 NET

And you also were included in Christ when you heard the message of truth, the gospel of your salvation. When you believed, you were marked in him with a seal, the promised Holy Spirit.

Catholicism believes in the One True Church. All the Catholic Churches in the city are part of one whole church. Membership can be about how active you want to be.

Protestantism believes all the protestant denominations are part of the Universal Church. You can go from placing membership from one church to another and yet be part of the Universal church. But membership can be a matter of salvation.

Good luck at choosing a church.

In 1 Corinthians 5:12-13 Paul says

12 For what have I to do with judging outsiders? Is it not those inside the church whom you are to judge? 13 God judges those outside. “Purge the evil person from among you.”

Church membership is how we know who is and isn't a believer. The church, as a whole, is charged with the task of declaring who is and isn't a believer based on their testimony. In Matthew 18:15-17 Jesus gives another example of the church having members:

15 “If your brother sins against you, go and tell him his fault, between you and him alone. If he listens to you, you have gained your brother. 16 But if he does not listen, take one or two others along with you, that every charge may be established by the evidence of two or three witnesses. 17 If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector.

How are we to know who is or isn't a believer if we don't have membership? The ability to exclude someone from the church means that there was also inclusion/membership/a group defined as "the church". Here are a couple other verses to consider when thinking of church membership:

Acts 5:12-13: “Now many signs and wonders were regularly done among the people by the hands of the apostles. And they were all together in Solomon’s Portico. None of the rest dared join them, but the people held them in high esteem.”

So, people faced the decision of whether or not they would join the church in Jerusalem.

This joining is more public and definite than an informal association.

2 Corinthians 2:6: Paul talks about a man who had been excommunicated,

“For such a one, this punishment by the majority is enough, so you should rather turn to forgive and comfort him, or he may be overwhelmed by excessive sorrow.”

A majority can't have decided on the exclusion unless there was a definite set of individuals who could make that decision as a church.