Question: "Didn’t the Old Testament punish blasphemy with death? How is that different from radical Islam?"
Answer: Leviticus 24:16 says, “Anyone who blasphemes the name of the LORD must be put to death. The entire assembly must stone him. Whether an alien or native-born, when he blasphemes the Name, he must be put to death.” So, yes, the Mosaic Law did require the death penalty for those who blasphemed the name of God.
First, we must remember that the Israelites in the time of Moses lived under a theocracy. God's people in the Old Testament prior to the coming of Christ were identified externally through their adherence to the Law. The theocracy encompassed everything from ceremonial religious rites to civic bylaws. The Law regulated dress code, diets, relationships, contracts, and even benevolence. The Law provided harsh penalties for wrongdoing, including the sin of blasphemy. One of the purposes of the Law was to establish the conviction that God is holy. God’s name, as an expression of His nature, is also holy (Psalm 99:3; Luke 1:49).
The coming of Christ signaled a transition in how God's people are identified. They had been previously identified through the Jewish culture and a theocratic marriage of “church” and state. With Jesus came the New Covenant, and God’s people were identified internally: “The kingdom of God is within you” (Luke 17:21). In order to provide open access to God, Jesus fulfilled the Old Testament Law (Matthew 5:17). No longer were sacrifices necessary because He was the once-for-all sacrifice. No longer were specific dress requirements necessary. And no longer were God’s people identified by a state under theocratic rule. Certainly, the spread of the gospel was aided by the fact that it didn’t require an overhaul of the state governing authorities in other nations.
Christianity is not to be associated with revolution on a civil level. This is the problem with Islam. It can only be spread through conquest and forced submission. Faith is not required, only surrender. This is disingenuous and oppressive. Christians are instructed to submit to the governing authorities (Romans 13) and to work within the political system. The government was never intended to be a means of evangelism. The church is. And the church must be flexible enough to adapt to any culture. Christianity translates, whereas Islam dominates. Any religion that relies on the power of the state to ensure adherence obviously has no confidence in the power of its God to rule hearts.
Christians do not seek a theocracy nor should the church overly concern itself with civil/legal issues. We can speak on civil issues, but enforcing civil law is not our business. By the same token, respect for God, tithing, church attendance and other outward expressions of personal piety are not civil concerns. Jesus nullified the theocratic approach because it had served its purpose. He in turn established an ecclesiastical approach because only the local church can effectively reach local peoples within the context of their particular customs and circumstances.