The Democratic Progressive Party - during its eight-year interregnum (2000-2008) - re-branded Chiang Kai-Shek Memorial Hall as "Taiwan Democracy Memorial Hall" It renamed Chiang Kai-Shek Square as "Liberty Square." It was meant put the country's dictatorial past behind and highlight the way to a democratic future.
But the KMT Old Guard were up in arms (literally) and the best the DPP could do was paper over the past... literally. When the KMT got back in office (they were never out of power) the first thing they did was reinstate CKS and his family (wife Soong Mei-ling and son Chiang Ching-kou) and as the unholy trinity.
Chiang Kai-Shek Memorial Hall now has a souvenir shop where you can buy the idols for your home shrine: Chiang Kai-Shek, Chiang Ching-kou, and Sun Yat-sen. Even Mao Tse-tung. Don't be surprised - the KMT has been in bed with the Chinese Communist Party since the KMT lost the presidential election in 2000.