Many sects of Christianity seem to include the idea that believers need to spread their beliefs to non-believers, so if you just allow people to commit suicide

Many sects of Christianity seem to include the idea that believers need to spread their beliefs to non-believers, so if you just allow people to commit suicide (which the religion deems abhorrent), then that basically means the believers failed in their mission. It's the same reason that religious societies (including Christian ones) tend to try to push their religious values into law, instead of allowing citizens to choose freely.