There is a very small circle of researchers who find merit in this kind of work, folks like Busby and Helen Caldicott (whom I admire for her work in the '80s against the nuclear arms race, but who makes a lot of ill-founded proclamations about radiation hazards that are not remotely accurate). Mangano and Sherman are certainly widely-known - it's easy to become widely-known by making startling claims - but that scarcely means the respect they receive comes from mainstream scientists (which it assuredly does not).
As for the rest, of course radiation can have all those deleterious effects. Nobody is saying it doesn't. But the magnitude of the effects depends on how much exposure to what kinds of radiation. (There is debate about exactly what the dependence is, but this isn't homeopathic medicine here!)
The activist you quote (who himself is presuming to speak for the deceased Mueller) engages in exactly the same kind of specious argumentation that would flunk any budding scientist out of a basic course on data analysis. The US national debt has been rising continuously over the same decades that "sperm counts, sperm viability and fertility rates worldwide have been dropping;" do we therefore conclude that the US national debt is the cause?
Or do we instead think in terms of what putative causes might plausibly be expected to have those effects, estimate the relative magnitudes of those effects, and focus further study on the most likely causes? The answer depends on what the goal is. If the goal is to support a pre-ordained conclusion, the answer differs from the one that applies for someone trying to actually understand a given trend.