As a permanent resident in Japan, I'll bite.
The quote this is apparently based on is from 2001. Since at least 2010 Motegi has veritably and quite vocally been against the giving foreigners the vote. He is establishment LDP and they are hard right wing conservatives, some of them quite virulently anti-foreigner (read as: ethnically Chinese/Korean).
Why this particular quote has been dredged up now I can only guess.
茂木敏充外務大臣「外国人に参政権」は2001年頃の発言だった | 銀鼠ニュース
(I guess this can be google translated by anyone interested).