If you wonder about the importance of evidence to secular people, think about this: A whole world full of people waits out there, lurking to pull all kinds of shenanigans to get you converted to strange beliefs and practices they uphold, or to part with your money, without any kind of demonstrable evidence. The best they have is stories some unknown talebearer told that another unknown person wrote down. You get to choose from actual thousands of those doctrines in all their variations, but most people settle for the one chosen by their family in ages past.
So much for the importance with which people regard religion; it speaks more for the trust we have for our parents, that we typically never question their choice until well after we have achieved adulthood or have been exposed to the wide array of alternatives. With nothing else to go on, most people will switch for emotional reasons (“I like these people better”), because they relocated (“We couldn’t find a 5th First Columbia Baptist Pentecostal Refuge anywhere and we looked everywhere”), or because of doctrinal points (“The new preacher insists the creation story is metaphorical. That’s an insult to the truthful nature of the Bible with which I disagree.”) The few remaining wanderers have grown disillusioned by the universal insistence upon faith without evidence. Most have simply abandoned their religion because it seemed unconvincing or fake. The smallest number of them will adopt the atheist label after years of avoidance.
Once a person attaches dissatisfaction with faith-based beliefs to failure of their messengers to be convincing, and then sees how that failure stems from absence of any kind of real evidence, the importance of evidence becomes clear and the search for evidence-based beliefs begins.
None will be found. The seeker learns, instead (and despite misuse of language) to accept that something “is true based on this evidence;” and “accept that as false as shown by evidence;” or “accept those as farcical because of no demonstrable evidence.” Evidence gives science (and other practices that depend on it) a powerful tool with which to demonstrate its findings. By banishing a need for belief (but not belief itself, as that remains internal to each person), science as a process has freed itself to advance with constantly polished findings into the future.
The shoe is now worn on the other, correct foot. Evidence will fill the vacuum left by abandonment of belief and enlightenment begins for those who continue to learn. Unevidenced artificial ‘truths’ get cast aside one by one as the new seeker unearths new facts, more quickly for some than for others. Harassing challenges issued by believers alert the diligent seeker to what (s)he needs to know and speeds up the process. Never discount the value of that.