China needs to quietly support and build relationship with the sane political sides and their media enterprises in these two countries. The US has been at it for decades, since WW II. A lot of this hostility to China is manufactured by these US stooges in these countries and their media brainwashing:
Politics of South Korea - Wikipedia, the free encyclopedia
The current party in power, Park Geun-hye's Saenuri is the right wing party that supports US agenda in this region, while DUP is more friendly with North Korea and supports the Sunshine policy of unification, spearheaded by Kim Dae-jung. Common people in South Korea support DUP, whereas Saenuri has the Christian vote and the vote of senior citizens who feel some loyalty to Park Chung-hee, father of Park Geun-hye and of course this is also the party that get support from most Chaebols.
Note that the gap is closing between the two party's in most recent election and there is a good possibility that DUP will come to power next election.