The RP Witness article is beyond a paywall, so I can't respond directly, but you can find the article here: https://rpwitness.org/trunk/page/article/your-covenant-and-the-new-covenant
A similar article that I'll respond to more directly is here: https://www.thegospelcoalition.org/article/is-church-membership-really-required/ the argument is very similar to John Edgar's argument in the RP Witness.
Remember, the primary Evangelical tools of cognitive dissonance are equivocation and false dichotomy. With that, let's dig in:
The argument of church membership being mandatory is not whether we should or should belong to the "body of Christ" that is, the invisible church, the collection of all believers. The question is whether Christians are commanded to make vows to a local organization called the church. For example, in the RPCNA, you cannot make a profession of faith without also joining the church where you are making that profession. It is a reason why I did not profess faith when I felt a personal connection to Jesus beyond being raised to belief - I did not want to join my parents' church.
Israel is the church and the church is Israel - when Reformed theologians look at the church, they see an unbroken connection between the OT and NT church. Moses was a Christian just as Cornelius was the heir of Abraham. In the OT, the Jewish leaders confused ethnic Israel with salvation, just as the modern-day church has struggled with the connection between membership and salvation (remember Doug Wilson's "Federal Vision"). For both OT and NT, membership in the church was either by birth and acceptance of the covenant - what Rick Gamble would call "age-appropriate faith", or by accepting the sign of the covenant (circumcision or baptism) as a new believer.
So, let's understand that the "congregation" of Israel was never some individual isolated community, but was a nation, an ethnicity*, and a religion. I will say that the ethnicity itself is fluid. Deut. 23:3 says "No Ammonite or Moabite shall enter the assembly of the Lord; none of their descendants, even to the tenth generation, shall ever enter the assembly of the Lord," now, remember that Ruth was a Moabite, meaning that her grandson, David would be a second-generation Moabite, yet David was definitely part of the 'assembly of the Lord'. So, it seems the conclusion is that Ruth became Jewish by accepting the covenant (your people will be my people and your God will be my God (Ruth 1:16).
It's therefore important to understand that the ecclesiology in the OT and NT have to match. It took a number of families to form a synagogue, and there was no guarantee that there would be enough people when the Jews were scattered to form these synagogues everywhere they might migrate, yet, they were still children of Abraham. In the same way, we send missionaries to foreign countries to establish churches, yes, but even if a church doesn't get established we wouldn't force a few converts to move somewhere else to join a local body.
The synagogue is an example of the local church, and the local church is an example of the synagogue - our modern church adopted the synagogue model, which was pervasive in the first century. I believe that there is evidence that the synagogue is not inspired as the model of the church. Jesus taught in the synagogues, and Paul's practice was to preach first at the synagogues (e.g. Acts 17:1-2). So, there's definitely the idea that the synagogue was a good place to share the gospel. However, many of the people Jesus converted, like Jesus himself, were rejected by the synagogue. For example, John 9:22 says, "the Jews had already agreed that if anyone confessed Him to be Christ, he was to be put out of the synagogue", so that synagogue was definitely not a "church". John 12:42 says that the Pharisees made people afraid to confess belief in Jesus, lest they be kicked out.
In some ways, Jesus and Paul acknowledge the importance of the local church / synagogue to Judaism/Christianity, but they also don't make it a matter of faith. The church should keep this in mind. What happened to the blind man who was kicked out of the synagogue? Did he lose his salvation as the RPCNA "outside of the church there is no ordinary means of salvation" would suggest? The Bible makes no such argument, in fact, the blind man worships Jesus and chooses Jesus over the Pharisees.
So, it's obviously going to be better to be in a local body of like-minded people who want to serve Jesus but we need to take another look at the synagogue. How many synagogues accepted Jesus? Perhaps one, the synagogue at Berea, but that is even in question, because the Jews from Thessalonica came and stirred up the synagogue against Paul. The track record is extremely poor for synagogues being places truly looking for the coming messiah! What if the same holds for the local church? That would be tragic, and I think we are looking at an Evangelical tragedy.
The visible church is ultimately a collection of like-minded people serving God, not a hierarchy or a boot camp - I want to be careful here. First, Jesus did not threaten those who would leave. In fact, it seems like he almost invited people to leave. After Jesus preaches a difficult sermon, comparing himself to manna, many of his disciples leave. He does not threaten or pursue him. He seems sad, and he asks the disciples, "you do not want to go away also, do you?" (John 6:67) Peter's response is the response of the Christian in a local church today, "Lord, to whom shall we go? You have words of eternal life." Jesus also says, "My sheep hear My voice, and I know them, and they follow Me" (John 10:27) and "A stranger they simply will not follow, but will flee from him, because they do not know the voice of strangers."
So, first, we establish that those of the flock follow the voice of Jesus. I believe they also follow Jesus's voice when heard through those who are faithful to Jesus, whether brother or sister, deacon, elder or pastor. When people do not follow the leadership, there are two main possibilities, the sheep don't hear the leaders talking with the voice of Jesus, or the leaders are speaking with the voice of Jesus, but the people are not sheep. There can be other mixtures of truth and error, of course.
So, when we talk about elders, there seems to be more of an organic nature to elders than the modern church portrays. Elders are people who are older in the faith, who have a life that demonstrates faithfulness and love towards the brethren. They do not need the force of membership vows or church courts or arbitration clauses, because they speak with the voice of Jesus and the sheep listen and heed. That's the bulk of it. I do believe that there needs to be a mechanism of accountability for all Christians, although mainly to protect the church from wolves - spiritual, emotional, physical and sexual abusers. The church needs to be able to say, be careful of Frank - he's emotionally abusive. Frank will most likely walk out the door, so they may need to tell other churches the same. I don't know quite how that works. What we see in practice, however, is that the main thing elders should be doing, holding each other accountable, is the last thing they want to do in the modern church. Instead we have the Catholic church moving abusive priests from church to church, the Southern Baptist Church moving abusive pastors from church to church, and the more conservative churches trying their best to hide abuse, protect abusers and trap the abused.
I also want to say that like-minded means followers of Jesus. There should be no other bounds. Many of the doctrines we fight over are of no eternal significance, so why not hold your own beliefs, but agree to partner with people from diverse backgrounds? Am I more effective as a Christian if my church is scattered all over town and I visit only those friends, or am I more effective if I join with a church that is less theologically in agreement, but has members nearby where we can fellowship and invite neighbors?
To equip against the Evangelical arguments, what we will expect to see is first, an equivocation between membership in the invisible church and membership in a particular visible church, and second, we will see a false dichotomy where membership = salvation and not being a member is damnation.