4th cousins share one set of great-great-great grandparents. It's far beyond the range where it would cause genetic issues above what exist between any two random people. Even a single cousin marriage really doesn't increase the risk of genetic issues by a particularly concerning amount, it's only in communities with either repeated cousin marriage or where closer relatives are reproducing that there's a problem. I don't even know any of my second cousins. Fourth? Forget it. This is genuinely not something we should be wasting our time on.
For some perspective, about half of the world allows cousin marriage, some with restrictions. That includes most of Europe, multiple states in the USA, Canada, Mexico, Australia, New Zealand, and Japan. It also includes nations in Asia, Africa, and south America. There are ethical concerns regarding consent with first cousin marriage due to the close relationship and I don't actually think it should be legal, if only for that reason. We don't allow siblings with no direct relationship (adopted, blended families where both partners have kids from previous relationships) to be romantically involved either and that's obviously not because of the risks of inbreeding.
People massively overestimate the risks of inbreeding, historically a lot of reproduction was happening between first cousins, because until just a few hundred years ago most of the people you knew would be, at best, second or third cousins. The real horror stories only really happen with multiple generations of incest between cousins and siblings.
TL;dr: there's certainly an argument for banning first cousin marriage on the basis of "why even take the risk?". But that is absolutely not a basis for banning more distant relatives, because you are no longer taking any real measurable risk. There's a possibility for genetic issues to pop up between any two random people in the world and, once a couple is more distantly related than first cousins, the "risk" introduced by "inbreeding" (fourth cousins reproducing is absolutely not inbreeding) is dwarfed by the random risk any two individuals have.