I am not so much opposed to membership, as I am to the intrusive application process mentioned in the OP.
In my view, the statement of faith and constitution of the church needs to be read and agreed upon before anyone joins the fellowship. That way, there is none who can rightly divide or cause dissension because they may not agree with the direction the church has stated is foundations for being a local assembly.
Back in the day, independent Baptist pastors that started a church would hold title to the property of the church because there were some wolves that would come and join and then as the opportunity came, rise against the pastor, kick him out, and take over the church.
I saw in SB churches some very modernist groups get extremely upset when some investigated their founding documents and showed how very far from them the church had strayed on doctrine.
Does a church need a "background check" on new members, given that predators abound? When does such a check become intrusive when a debt to society has been paid?
I can see the need for someone to be able to write an account of them being saved, and I also can agree that some family information may be helpful.
But again, these should be "optional" and not a requirement.
The only must, should be agreement with the Statement of Faith, and Constitution.