Christianity is supposed to make a difference in peoples values, opinions, motives, and lifestyle. As such, it is expected to provide every area of their life. At the same time, we hear from Jesus that he fully expected that if his disciples were faithful, it would make a positive difference in society.
A Christian should have the same opportunity to influence society as anyone else. Anything short of that is discrimination on the basis of religion. A study of history shows us that despite the many abuses and wrongs that Christians have done through the millennia, they are far outweighed by the good that Christianity has brought to the world: hospitals, educational institutions, the system of law, sublime literature and art, the sense of justice and morality, etc. An objective study of history will show that it's a good thing that Christians had power and influence in secular affairs.
At the same time, there is hardly a more important civil principle than the separation of Church and State. History shows us that when the two are joined, there is nothing but problems. Separation of Church and State is not only wise but necessary.
> Since Christianity basically functions to regulate human behaviour and provide hope through the gospel of God
I'm sorry, but this is not how Christianity basically functions. Christianity's basic function is to show how a person's sins can be forgiven and how that person can have a relationship with God. the hope the gospel provides is the hope of freedom from sin in a relationship with God. It really has nothing to do with morality or government, civility or society. End it is precisely because peoples sins are forgiven and they have a relationship with God and are made new in life that they are such a good influence on society and their involvement in civil affairs.
> Should Christians be allowed to bless nuclear weaponry (like the Russian Orthodox Church)?
Absurd nonsense if you ask me. (Oh that's right, you did ask me.)
> Should Christian denominations be allowed to voice their opposition on conflicts and unfortunate scenarios (like 2014 Crimea occupation and etc)?
Absolutely. We should be the voice of wisdom, reason, and Justice.
> Should Church leaders be allowed to run in secular politics again (like the Catholics during the 60s)?
Absolutely. That's what democracy is all about. Anyone can run, anyone can win. To shut Christians out on the basis of religion is blatant discrimination. Presumably what a Christian brings to the table is reason, wisdom, morality, compassion, justice, and discernment.