I am glad we share a view in part of the Kingdom being prominent in our gospel being presented.
I am constantly reworking my views here as it is a work in progress.
I have posted a few quotes from Abraham Kuyper on what became known as sphere sovereignty.
He ran into opposition it seems, I am not sure why?
I am not very familiar with Kuyper, but have been reading up a bit on "Sphere Sovereignty". So I am responding in part to work through "Sphere Sovereignty" (for my benefit and clarity) and to answer your question of why I believe the concept may run into opposition.
If I understand correctly (please let me know if misrepresent the thought) the idea is that there are distinct "spheres" of life and these different areas or realms interact but stay separate. Kuyper believed that there are a variety of God-created structures like family, church, state, business, etc. These are distinct spheres with their own unique method of functioning. Each are accountable to God within their own sphere.
InterVarsity offered this illustration:
We have an example of having a father working for their son. In the home, the father is the head of the household and can properly tell the son what to do and not to do without overstepping any boundaries. However, when at work, the roles must be reversed. The son becomes the authority over the father and can (should) dictate what behavior is appropriate for the father. This can lead to tension, but if we respect the spheres properly, there should be no tension.
So, if I understand correctly (a BIG if) it relates to the OP in that the sphere of world politics is a distinct sphere which touches and interacts with other realms yet remains distinct unto itself and is accountable to God in its own function and operation.
The Church does not control the State (it is a separate "sphere", no less accountable to God in its operation and function). Therefore the Church has no business (as the Church) in dictating the affairs of the State, however the State is nonetheless responsible to God for its activities. A pastor of a Church functions not as a political figure but as a pastor (accountable to God as the pastor). If the pastor is also a politician then he functions as a politician (accountable to God as a politician).
I suspect there are a couple of reasons Kuyper met opposition. The Reformation carried with it some ideas from the RCC. It reformed some ideas (like communion, atonement, etc.), rejected some things (like the Pope as a vicar of Christ, a works based justification, etc.) and maintained other things (at least initially and to some degree). One of these things the Reformed Church initially maintained was the idea that the secular government (the State) was an "arm of the Church". Those with this view probably resisted Kuyper in treating these spheres as separate from the authority of the Church (just a guess).
I personally have an issue with the idea of these "spheres". I do not agree with the idea that these spheres are separate realms. When it comes to secular government (politics) I place them in the realm of the World (principles and powers that are hostile, at enmity, with God). As such, I view Christians in politics as a compromise that should not be made. I am tempted to appeal to the early church for this model as the early church abstained from politics, from serving in government, from voting, military service, etc.. BUT at the same time that does not mean that we should. The early church worked within its own context and interpreted Scripture through what they experienced. I also have read quite a bit of Anabaptist theology, which could have influenced how I personally interpret this issue. I try to be objective, however we are all influenced by our experiences, to included theological arguments that have been persuasive in our own lives. Still, I do share their interpretation of the role of a Christian. Whether right or wrong, those are my convictions.
Here is where I stand regarding cultural-engagement: I believe that we are to engage culture insofar as we are reaching people in these cultures with the gospel of Jesus Christ. I do not believe we are called to make the World better, but we are called to make the world a better place insofar as the people we reach. The World is condemned and perishing, the Kingdom is here and coming.
I think that the best witness we have is explaining why we hold our positions.
I do not vote or participate in the political system because I am a child of God, a citizen of His Kingdom, and believe for me to do otherwise would be a compromise (one "foot" in both "worlds").
That said, I can appreciate when Christians do participate in politics in order to influence others with the gospel message. I do not have to agree with their actions, but I can appreciate that they are doing it for God, just as I hope they can appreciate that I am refraining for the same reasons.
Sources:
Whatever Happened to Sphere Sovereignty?
Introducing Kuyper's "Sphere Sovereignty" - Emerging Scholars Blog