I completely agree with you. There is one point though which is of interest: It is impossible for the truly secular state to be “separate” from the religious, because religion intervenes fundamentally in the lives of a mass of people. It is in conflict with secularism precisely because there is no such thing as religion being “personal” — by definition. Its fundamentals are meant to be obeyed by a mass of people, not merely practiced by willing individuals. Or rather, the practice is in the propagation and imposition.
The other side of the argument is that secularism is also not merely a personal philosophy, but one that seeks to intervene in the lives of a mass of people. At least, that is what “state secularism” is. But without the force of state power behind her, the individual secularist will be destroyed by the very fundamentally non-personal nature of religious faith.