Hollywood is not wrong that moisture loss is bad for bread, it’s not the primary reason to avoid refrigerating bread. The science: Refrigeration speeds up the starches’ return to a more organized crystalline structure (also known as retrogradation), which means it hardens (i.e. stales) far faster.
Unrefrigerated bread does typically get moldy faster. The trade-off is longevity over texture, and many consumers are more concerned with stretching their bread (and their metaphorical bread) as far as possible, especially these days.
To which we say, fair. And also: freeze! Becky wrote a helpful guide to storing bread in that other section of your favorite appliance. She says the freezer “serves as a kind of pause button, meaning fresh bread you move into cold storage can come out almost as good as the day you put it in.”
Serious Eats also covered the issue to the same conclusion a while ago: https://www.seriouseats.com/does-refrigeration-really-ruin-bread
I put sliced bread in the freezer and thaw slices as I need them in my toaster. Works pretty well, haven’t thrown away moldy bread since I started doing that