In so far as I understand it has been studied, or rather attempts have been made to study it, and they have uniformly failed because the phenomena as described by masturbation-fearers does not exist in any meaningful way. It really is just mormons, catholics, and other weird little freaks trying to pathologize normal sexual behavior. It has legs because so many people have absolutely no concept of what normal sexual behavior is, and because everyone's so damn isolated and porn is stimulating enough to consistent help cope with the social and cultural wasteland of 21st century life. People think they're jerking it too much because they've been conditioned to feel intense shame for jerking it at all, and they think they're addicted because they think about sex a normal amount of the time. There's a pretty strict physical limit on "jerking it too much" because no matter what you use for lube chafing will make itself known eventually.

Depression, anxiety, and malaise also factor in - Masturbation is a very basic form of self-soothing available to almost everyone. People who are already in bad headspace and beset by religious brainworms masturbate because it makes them feel better, then once the anxiety and self loathing comes back htey ascribe it to masturbation and decide they're weak, pathetic, sinners, addicted, whatever bullshit because otherwise they wouldn't masturbate to feel better or distract themselves from the depression. And then they go a step further saying that masturbation and thinking about sex is a source of depression.

It's really just weird Christians convinced that if you eat enough bran flakes you won't think about sex, updated for the 21st century.