From the first article linked, there is a single informant that claims nuclear material was aboard a scuttled ship. The article as linked provides no further information, but mere allegation is sufficient for mdsolar to blame nuclear power.
In the actual article, one will note that there is no actual speculation about the Yakuza having any ill-intent. Indeed, it seems to be a general article about how the Yakuza win contracts in construction and cleanup. And after a massive earthquake and tsunami, there's lots of cleanup to be done.
As an interesting aside, he article claims that the Yakuza get 3% of the total construction in Japan. I see no reason to suspect that wouldn't include projects related to all forms of energy. I trust mdsolar would agree with my "Japanese solar power in bed with organized crime" headline.
There are legitimate gripes about nuclear power. Indeed, the numbers I've seen suggest operating costs that aren't substantially below any other forms of energy. But the sort of fear campaign spread by mdsolar (someone who himself stands to profit from such fears, see his profile for links) is unacceptable.
Marriage is, by definition, not a private institution, but a public one. Being married doesn't affect what you do inside your own home (to be taken as an idiom for things that don't affect others), it affects how society interacts with you. I therefore think it is disingenuous to claim that it is not a social issue, outside the purview of societal interest.
That's not to say that it should be regulated, in this case or any other, but I merely wish to indicate that the question is not itself injurious, as you seem to say.
Weekend, where are you?