Why should Israel punish heretics with death? in the NT it does not seem to happen in the same way. Should a Christian country tolerate pagan philosophies and religions, or should you pursue for the good of all?
First of all, let me acknowledge that the distinction you notice is certainly real. The New Testament approach to heresy and to sin in general is not the same as in the Old Testament. I would like to suggest three reasons for this:
1. The nature of Israel as a theocracy.
2. The nature of progressive revelation.
3. The physical versus spiritual divide between the Old and the New Testaments.
One reason that the way to deal with heresy (and other violations as well) is different in the Old Testament is that with the Jews it was assumed that the entire population, at least nominally, were the people of God. They were governed, whether during the period of judges or the kings, by Jewish leaders. This was a Jewish state. Therefore, one could assume that every citizen was being governed by leaders appointed by Yaweh. In such a situation, God can hold the people in the kingdom to godly laws. Such is not the case for Christians. We do not live in countries where we can assume that all people have voluntarily submitted themselves to the rule of God. Our secular governments cannot be expected to enforce correct doctrine or Christian concepts of morality. In such a situation, the New Testament has teaching about church discipline, such as expelling people from the community for certain gross sins, but there is no legal authority in the church. This will go some ways to answer your question.
Then there is what is sometimes called progressive revelation. As we move from patriarchal times to the Jews under the Law of Moses to the Church under Jesus and the New Testament, God has progressively revealed his will for us. Matthew 5:21-48 is a good example of this. Due to the primitive nature of the earlier Jews and due to the cultural background, God allowed for them to divorce, for example. Jesus tells us not only not to divorce, but also not even to lust, whereas in the Law of Moses the command was not to commit adultery. For harsher times, there were harsher penalties in the Law of Moses. The Old Testament was written in a backdrop in which Jewish leaders were the police, enforcing social order and Jewish armies were defending Jewish territory is a world that was more brutal than ours today. All this is very different for us. Again, this will go some way toward answering your question.
Then there is the general principle that in the Law of Moses, both the blessings and the curses were principally about physical things, whereas, in the New Testament, the equivalent blessings and curses are almost completely of a spiritual nature. The Jews defeated their enemies. We convert our enemies. The Jews were promised homes and land and stability. Our promises are more about spiritual blessings and future blessings. Even the legal system of the Jews involved more physical punishment rather than God’s discipline or even future rewards or punishment. This also explains the physical punishment in the Law of Moses and the lack of any equivalent at all in the New Testament.
By the way, scholars tell us that the Jews very rarely applied capital punishment. Jewish elders almost always found a way around applying the highest penalty. There is no evidence, for example, that a child was ever executed for disrespecting parents or that idolaters were given capital punishment. The proposed punishment seemed good enough to the Jews and they almost never applied it, at least as far as we know from the historical records we have.
Now, let me address the rest of your question. I believe that there is no Christian country. Even when there supposedly was, for example in the late Roman empire or in Europe in the Medieval Period or even in the sixteenth and seventeenth century when Christendom was still in place, there was no truly Christian country. I doubt that any of these nations ever had more than ten or at most twenty percent of real disciples of Jesus. I am not saying this to judge anyone in particular, but we are talking about reality here. As Christians, we are not in charge of our countries. We cannot or at least we should not impose our doctrines on non-Christians. This does not make sense to do so. People who have not committed to being a disciple should not be forced to behave like a disciple by Christians. Only a small proportion of any country will be Christians. The vast majority will either be fully pagan or will be only nominal believers. Christians have no power over these people and it is not clear that we would want to have power over these people even if we could, because our kingdom is not of this world. Here is the key difference. The Jewish kingdom WAS of this world. God’s kingdom is not of this world.
There are countries where Christians can vote. And occasionally, there may even be a Christian in a place of high political power. We can influence the directions our nations go. If we live in democracies, we can vote for policies which are friendly to Christian ethics and morals, but we should never assume that this is our principle means to influence our world. Our churches are “cities on a hill” but they are not the entire culture. Our weapons are not of this world, as Paul said. We can vote against legalized abortion. We can vote to help the poor, to limit the power of the wealthy, to help the immigrant and those who are generally abused by those in power, and we should do those things, but we cannot reasonably expect that the places where we live will ever be “Christian.” As Christians, we do not agree with marriage between two people of the same sex, but we cannot assume that the majority in our culture will agree, and it is not clear that we should impose this morality on those who are atheist, even if we could. That is a matter of opinion, I suppose. Therefore, as disciples of Jesus, we will have to do more than merely “tolerate” pagan and other philosophies, we will have to live in a world immersed in these unchristian ideas. The early church did this and they thrived greatly. We can as well.