To be fair, it’s not completely made-up. There is a body of evidence that suggests that even non-ionizing EM radiation may have so-called “biological effects” in humans.
Organizations like the Environmental Health Trust have been banging the “cellphones cause infertility and cancer” drum for years, and cites numerous studies on their website.
Of course, much of this research is of questionable relevance to real-world use cases involving actual phones and actual humans as opposed to, say, a bunch of rats being exposed to low-power microwaves in a lab for hours on end, but it exists nonetheless.