I don't know about the Detective Conan bit, but the Pokémon part is that the Pokémon website has (had?) a feature where certified people can setup TCG events, and someone organized one at the Yasukuni Shrine, the one for the war criminals.

Chinese people on the internet were upset, China made a statement, the Pokémon Company apologized

Now personally I think this is less on Pokémon and more on Japan having a shrine celebrating pillagers and rapists.

EDIT: Looks like the reason people are upset over Detective Conan is that they did a promotional crossover with My Hero Academia, and in My Hero there's a character named Maruta Shiga who does human experiments. Maruta (literally "log") is what the "scientists" of Unit 731 called the people they killed.

The shrine commemorates the 2.5 million Japanese soldiers who died in war, including 30,304 Taiwanese

This is the real reason , it still do not justify chinese autority actions

What’s Detective Conan? A barbarian detective movie?