Unfortunately, it is not only the public-at-large that thinks science and religion are compatible. Many scientists also are religious. You may ask, why do I have a problem with this? Simple: science has falsified all interventionist religions. Thus, what religious scientists are doing is compartmentalizing. Even some members of elite scientific organizations of the "hard" sciences are religious (link).
All of this sad state of affairs is why I promote science-based thinking and do not look at individuals' views on religion. I urge that one not look at individual scientist's views on reality but what science itself is actually saying about it.