Creationism and ID are explicitly banned but so is proselytising even in religious education classes. The Qur’an may not be taught as if it is true even in Muslim independent schools, nor may the Bible in Christian schools. The decision looks like a really startling attack on the right of parents to have their children taught what they would like. Of course it does not go so far as the Dawkins policy of prohibiting parents from trying to pass on their doctrines even in their own families - and, if it did, it would certainly run foul of the European convention on human rights. It does not even go as far as Nyamko Sabuni, the minister for integration - herself born in Burundi - would like: she wanted to ban all religious schools altogether. But it is still a pretty drastic measure from an English perspective.
The law is being presented in Sweden as if it mostly concerned fundamentalist Christian sects in the backwoods; but the Christian Democratic party, which represents such people if anyone does, is perfectly happy with the new regulation. There is little doubt that combating Islamic fundamentalism is the underlying aim, especially in conjunction with another new requirement that all independent schools declare all their funding sources. This would allow the inspectors - whose budget is being doubled - to concentrate their efforts on those schools most likely to be paid to break the rules.