Oh boy, am I about to get myself into a wild mess here!
I am not sure it is wise to make a single dicipline case, even if it involves a giant like Beeke, the lense through which we jufge three entire denominations. Are you bringing this up because you think it is illustrative if a larger issue in Dutch Calvinism or this subset of it? If so, can you be more specific than "too conservative"? Or just because for most on the puritanboard this is the most familiar name that has something to do with these groups?
Basically all of the above! For better or worse, most but not all of the major Dutch Reformed secessions and denominational foundings were closely identified with key individuals. Ledeboer, Kuyper, Kersten, Hoeksema, Schilder, and Beeke all differ in many ways, but their denominations took on key aspects of their life and ministry. That is in some ways good and others not. It's not like the OPC where Machen was a huge influence but his death led to multiple splinterings, and the modern OPC has numerous sources of its key principles, or like the URC where there were easily a dozen key leaders of the secession, and then the people came in associated with Westminster Seminary in California who brought a different approach from that of the earlier seceders.
The Beeke situation is very complicated and anything I write is guaranteed to get pushback if I post it here because it needs to be twenty or fifty pages with a ton of footnotes to be complete, but this will likely be enough for your purposes. Suffice it to say that the two key underlying issues in the Beeke controversy were the free offer of the gospel and whether a minister with a legitimate biblical divorce can remarry and remain a minister. Officially, the NRC synod said "yes" to both. But a lot of people remained seriously unhappy and that put Beeke in the crosshairs. And yes, I say that with bias toward Beeke because I believe he was right, after reading huge amounts of stuff and probably digging into the case more than anyone who wasn't on the synodical investigative committee or Beeke's own consistory. I believe Beeke was abused and is a godly man who was patient beyond what anyone should have to tolerate. Others disagree, and that is what caused the division in the NRC.
Why is that? Is there anywhere where I can read about this man without having to learn Dutch first?
The simple answer is I can send you to Google to look up GH Kersten and the Gereformeerde Gemeenten and his role as a member of the Dutch Parliament in attacking Abraham Kuyper's view on civil cooperation with Roman Catholics, and before that, to Mulder's timeline on how Kersten unified several "Dutch Puritan" groups into the Gereformeerde Gemeenten as a denomination. You'll get some formal answers. Also, a book of his Heidelberg Catechism sermons has been translated into English. That will give you a good sense of his theology of the need for a deep personal conviction of sin.
However, to TRULY understand the Dutch at a deep level, you must not only learn Dutch, but live among the Dutch, to know what "lives" in the churches. With the smaller denominations, there are not many (if any) books written in or translated into English and that's a real problem.
I have an undergraduate degree in theology from Calvin College. I spent three years at Calvin Seminary before dropping out, due largely to extreme frustration. I spent ten years of my life working for Christian Renewal magazine, which was at that time the main conservative news organization reporting on the CRC and the people seceding from it. During that period I reported not only on the CRC and RCA and the URC (as it developed) but also attended almost every OPC General Assembly and NAPARC meeting, and covered the NRC synod that deposed Dr. Beeke, and reported on the beginning of Puritan Reformed Theological Seminary.
Even all that is not really "enough" because I can't read Dutch and that cuts me off from key things I should know, and forces me to rely on secondary sources, with their inherent biases, rather than being able to read primary source documents.
Things are a little different now that the "older generation" has passed which was still fluent in Dutch and regularly read Dutch theology and maintained contact with immediate family in the Netherlands, but you'd have to actually live in Grand Rapids, or Northwest Iowa, or certain other key places, to really understand the culture.
You live in Israel. I assume you speak fluent Hebrew. Ask yourself how easy it would be to understand the various Hasidic Jewish groups in Israel without speaking Hebrew and living among them, and you'll have your answer about understanding the more conservative groups among the Dutch Reformed -- and for many of the same reasons.
A church that emphasizes covenantal faithfulness over many generations, and has its own Christian schools, and successfully enforces a need to marry within one's own faith community, or by way of exception, an "uitlander" who has been willing to FULLY (not just nominally) join the covenant community, and become a 200-percenter advocate of its core distinctives -- well, let's just say there are both sociological and theological reasons why for many centuries Dutch Reformed people and Jewish people have gotten along better than almost any other religious group has gotten along with Jewish people. Obviously there is no shared faith in Christ, but a church that takes VERY seriously the Old Testament standards for business, personal and family life is going to develop some distinctives which will look a lot like the Old Testament people of God, and that's ESPECIALLY true in diaspora settings, such as the Dutch Reformed expatriate communities in the US and Canada. Let me be clear that I'm complimenting the Dutch here, not criticizing. Teaching children the importance not only of personal conversion but also hard work, raising children in the nurture and admonition of the Lord, biblical standards for marriage and family, and a whole host of other things are good, not bad -- but also VERY different from much of modern American evangelicalism which is all about "me and Jesus" and not a covenantal community of faithfulness.
Now when I write these things, understand that I am myself an "uitlander." I grew up as an Italian in Grand Rapids. I was converted as a young adult, became Reformed by reading Calvin's Institutes, and then was confronted with a very real problem of "Where do I find a Reformed church that actually believes what this book teaches?" Not an easy thing to do in Grand Rapids in the 1980s. The churches that were open to outsiders like me were either running after Robert Schuller, or broad evangelicalism, or Barthianism, or outright liberalism. The churches that were confessionally Reformed were hard to find (remember, this was before the modern internet) and many were small and not interested in non-Dutch people. That's nothing like Grand Rapids today, but it is the community I grew up in and I know it well. I'm not being fair to Dutch conservatives today -- Dr. Beeke's own church, for example, has an ethnic Chinese congregation worshipping there -- but when I was converted, I had been walking past the Crescent Street NRC for years and I knew full well that non-Dutch people were not wanted. Dr. Beeke's predecessor was not Dr. Beeke, and it took many years for Dr. Beeke to make the church what it is today. I'm not going to name names, but I actually visited most of the main conservative non-CRC churches in Grand Rapids in the years before the secession began, and there are reasons why I did not join the CRC. I probably visited about a dozen or so churches that were known, in the 1980s, for being more conservative than the CRC, and what I saw then is not what I would see today. Most of those churches are either dead or a much better church than they used to be.
As one of my professors at Calvin said, "You can explain the Christian Reformed Church by sociology, not by theology." That isn't fully true of the more conservative bodies, but it's not wrong, either.
Hope this makes some sense. I think, honestly speaking, the parallel to what you see in ethnic Israel is going to make more sense to you than it will to most Protestants because you live in Israel, and again, understand I'm saying that as a compliment, not a criticism.