Once they went so heavily into (Shitty) reactors, I think their main problem morphed into the presence of nuclear ordnance on board rather than the power plant. Don't know if that's still the case or not.
I seem to recall New Zealand's refusal to allow nuclear-powered vessels into their ports, a situation that pretty much nuked (no pun intended) a military treaty with NZ - ANZUS, according to Wiki.
As Crazy Horse mentioned elsewhere, Japan apparently changed its tune and allowed the USS George Washington to be homeported in Yokosuba. The Navy won't confirm or deny the presence of nuke weapons on board ship, of course, so Japan's concern appeared to be the presence of nuclear energy altogether - I guess.