靖国神社参拝 is a politically charged topic — visits by government officials to Yasukuni Shrine (which enshrines war dead, including convicted war criminals) are a recurring diplomatic flashpoint with China and Korea. に関しては ('regarding') is the formal scoping phrase. 閣僚 ('cabinet ministers') is political vocabulary. 自主的な判断に任せられている ('is left to independent judgment') uses the passive of 任せる ('to entrust'). The sentence describes actual Japanese government policy on this sensitive issue.