Doesnt christianity ban apostasy too, yet even the most conservative and reactionary Christian countries have no apostasy laws.
Christianity and Islam are two very different religions. In Islam, everything is about submitting yourself before God and believing in the oneness of Allah. Muslims see the Qu'ran and the words within it as being created by Allah and brought to humanity by the Archangel Gabriel through revelations to Mohammad. But despite Mohammad being a prophet, Islam strictly forbids worship of Mohammad as if he was God. When Mohammad returned to Mecca, the first thing he did was destroy the idols in the Kaaba. That is still celebrated by Muslims today, because as far as they're concerned, the only one who should be worshipped is Allah, no ifs or butts.
In Christianity, Christians do have a relationship with God, but that relationship is determined by how people interpret the teachings of Jesus, his disciples and the apostles. Christians follow the example of Jesus, his disciples and the apostles as they preached the word of God, so God is a supreme being within Christianity, but he is not the one focus of the faith.
Most Christian countries (that I know of) don't have apostasy laws because fundamentally, there is no such thing as a Christian theocracy in the modern world, except for Vatican City. Also, Christianity doesn't have a movement like Wahhabism and Salafism which says 'All Christians must worship the way Jesus did' and things like that.
But, I should point out that in at least five countries, Guyana, Suriname, Greece, Italy and Poland, which have majority Christian populations, blasphemy is still a crime. Even some US states still have anti-blasphemy laws on the books, but they're trumped by the First Amendment. These blasphemy laws, however, are not in accordance with religious teaching. It has more to do with their cultural roots than they do with actual scripture.
(Please correct me If I've got any of that wrong)