Good points: We can’t understand Shakespeare without the Bible, or Bach without Christianity.
And that might make for an interesting study of “secularism”. There is something there, without the Christian framework.
However, western philosophy, if stripped of religion, Decartes, Kant, Nietzsche, socialism, etc., all have critical breakdowns. They do not have substance except in relation to religion. Though most are a rejection of religion, they are nothing without it.
Much more success would be found in the East, where secularism goes back to about 500 B.C., both with Legalism and Confucianism. Yet both of these were far more harmonious with Animism, Taoism, Buddhism and multi-Theistic Hinduism, while each retained their individuality.
Secularism in the West didn’t get started in earnest until the 16th Century, and in the Muslim world only in the 20th Century, derivative of western secularism.