The reason why a Christian cannot take on the yoke of an unbeliever is that the Christian is living out of a different source of life. They are absolutely opposite - the life of Christ and the life of this world. God has made us in Christ to be risen in Christ with the life that seeks God. This life is not because of anything we have in ourselves. Christianity is not something that we did for ourselves.
Cults do things to people.
Philosophies do things. But Christianity is not something of ourselves, its origin is not of ourselves. Its origin is of God. God, by grace, has placed within the child of God a life different from the life that lives in the unbelieving world. Because of that life, we cannot, we may not, we will not put our neck in the yoke of an unbeliever.