Is 太君 a derogatory word?
It was a good word. For example, in 红楼梦 sometimes they call 贾母 as 史老太君. It was used to refer some senior with respect.

But during the war, those traitors started to use this word to the Japanese to show their respect to the Japanese and nowadays Chinese people don't like it anymore. The netizens use this world in a self-sarcasm fashion.

It is like the Swastika, which was used a lot in Buhddalism and can be seen a lot in ancient Buhdda sculpture. It was a good sign and then the Nazis started to use it and now most people will only associate it with the Nazi and don't like it anymore.