This, in my opinion, may well be one of the most crucial issues facing the church at all times. Should one keep the church doors wide open for all and sundry to find a spiritual home there, irrespective of having a credible profession of faith or does one restrict membership of the church to those who are able to give a credible profession of faith before the elders and the church alone?
Our 1689 Baptist Confession of Faith  states:
26.2 All people throughout the world who profess the faith of the Gospel and render obedience to God by Christ according to the Gospel, and who do not destroy their own profession by any fundamental errors, or by unholy behaviour, are and may be called visible saints.1 All local2 congregations ought to be constituted of such people.3
(1) 1Co 1:2, Act 11:26 (2) Original: particular (3) Rom 1:7, Eph 1:20-22
26.6 The members of these churches are `saints'1 by calling and they visibly demonstrate and give evidence of their obedience to the call of Christ by their profession and walk.2 They willingly consent to walk together according to Christ's instructions, giving themselves to the Lord and to one another by the will of God, affirming their subjection to the directives of the Gospel.3
(1) i.e. holy ones (2) Rom 1:7, 1Co 1:2 (3) Act 2:41-42, 5:13-14, 2Co 9:13
The Confession leaves us in no doubt that our Baptist Churches ought to be constituted on the premise that only the converted, regenerate or ‘born again’ ought to be admitted as members of the church.
The danger of admitting unconverted people into membership ought to be evident. When sheep are replaced by goats, then it is clear that goats will rule the flock, and they will rule the flock not according to the Word of the Great Shepherd, but according to their carnal nature and desires, replacing the word and the authority of the Great Shepherd with their own wisdom. This is exactly what has happened in many former evangelical churches as they compromised the standard of entrance into the membership of the church.
A Historical Example
Recently I acquired the works of Jonathan Edwards and I am finding this to be a fascinating read. The introductory section includes the Memoirs of Jonathan Edwards  in which his own experience in his church at Northampton, New England is described.
On the 22nd of June 1750 Jonathan Edwards preached his farewell sermon to his congregation in Northampton, New England. This was not a farewell sermon which he had preached upon leaving the congregation because he had received a calling to another church. No! This sermon was preached because the church had chosen to dismiss their pastor! The reason why this happened was that pastor and people ultimately differed concerning the qualifications for church membership.
It all started in 1744 when he was informed that some young people who were members of the church had “ licentious books in their possession which they employed to promote obscene conversation among the young people at home “ . Edwards was rightly concerned about this since these young people, being members of the church were corrupting others. So, after preaching a sermon to this effect , a committee of inquiry was appointed. The enquiry became guilty of procedural error and thus members of the church at Northampton whose young people had been subjected to this inquiry began to oppose Edwards and the inquiry. Edward’s biographer writes :
“This was the occasion of weakening Mr. Edwards’ hands in the work of the ministry, especially among the young people, with whom, by this means, he greatly lost his influence. It seemed in a great measure to put an end to his usefulness at Northampton, and doubtless laid a foundation for his removal …” 
There was however another difficulty of a far more serious nature. The church of Northampton , like many other early churches was formed on the basis of a ‘strict communion’, that is, only those that had a credible testimony of conversion would be admitted to the communion table, and only after due examination by the pastor and elders. Rev. Stoddard, Jonathan Edwards’ grandfather and his predecessor in the church at Northampton however made a change to this ruling in 1704 and in this he caused a problem for his successor. Stoddard introduced the notion that
“unconverted persons … had a right in the sight of God… to the sacraments of the Lord’s supper;… it was their duty to come to that ordinance , though they knew they had no true goodness or evangelical holiness. He maintained that that visible Christianity does not consist in a profession and he encouraged unbelievers to participate in communion on the principle that they regard the sacrament as a converting ordinance, and partake of it with the hope of obtaining conversion.”
Although Solomon Stoddard had faced initial opposition in departing from this old rule, yet due to his great influence (he had been their pastor for 32 years by then) , his view spread and, by and by, took hold of ministers and people in the county and other parts of New England. When Jonathan Edwards joined the pastorate at Northampton he had some initial hesitation over this matter, but did not pay sufficient attention to it until he began to study the Scriptures, coming to the conclusion that his grandfather’s position on this matter was wrong .
“ He was fully convinced that to be a visible Christian , was to put on the visibility or appearance of a real Christian … and as to the ordinance of the Lord’s supper was instituted for none but visible professing Christians, that none but those who are real Christians have a right, in the sight of God , to come to that ordinance… that none ought to be admitted who do not make a profession of real Christianity…” 
When Edward’s position had become known in the town there was a great outcry against him and calls were made to have him dismissed. When he wanted to defend his cause by preaching upon the subject he was opposed by the ‘standing committee’. He then proposed to put his argument into writing, but in the end it was read by a very few, and ultimately Edwards was dismissed from his pastoral charge.
Observations and Conclusion
When Jonathan Edwards had called the young people to account in 1744 the seeds of Christian nominalism had long been sown, as the church under Stoddard’s long pastorate had permitted the unconverted to participate in the full privileges of church membership. It is not easy to undo spiritual knots, once they have been tied. Many a good pastor has lost his pastorate due to resisting the unbiblical traditions of their predecessors. We saw that Jonathan Edwards did not survive this challenge, though we believe he was right in every way to ensure that the church be considered as a body of true believers.
I and our congregation continue to stand on the basis and foundation of our biblical confession of faith in this regard .
 THE BAPTIST CONFESSION OF FAITH OF 1689 Rewritten in modern English by Andrew Kerkham
 John 3:1-8
 These were compiled by Sereno Dwight , a later relative of Edwards in 1830
 The works of Jonathan Edwards: Vol 1 , Banner of Truth , p. cxiv
 For this purpose he preached on Hebrews 12:15,16 ( Works, p. cxiv)
 Edwards appointed the time for the committee to meet at his house and then read to the church a list of the names of the young persons whom he wanted to come to his house at the same time. Some of the names read were of the persons accused , and some of them were witnesses. Unfortunately he did not tell the church who was guilty and who was merely called upon as a witness. This caused a big commotion and much anger in the town of Northhampton.
 Ibid, p. cxv
 Rev. Stoddard had been the minister of this church for 55 years when Jonathan Edwards was ordained ( p. xxxvii) . He died on the 11th February 1729 (p.xl)
 Ibid . p. xxxvii
 Ibid p. cxv; see also pp xxvii
 Ibid, pp cxv- cxvi
 I find it interesting that reference is made here to a ‘ standing committee’ rather than an ‘eldership’.
 It was entitled : “ An Humble Enquiry into the Rules of the Word of God , concerning the Qualifications requisite to a Complete Standing and Full Communion in the Visible Christian Church”.