Some of these are not the best examples...
- Character simplification: This was a part of a wider progressive movement in the Sinosphere in general. Traditional characters were seen back then as a hinderance to raising literacy rates. In fact, the mainland's stance here follows that of Korea (which completely got rid of Hanja) and Japan (which tried, and failed, to completely remove Kanji). This was not done because the traditional characters are "old-fashioned" but rather to get the vast rural population to be able to read.
- Hokkien: This is a regional dialect imported from southern mainland China to Taiwan long before the civil war that split the two apart. After the war, regional dialects were suppressed _both_ in the mainland _and_ in Taiwan in favor of Mandarin (which is a northern dialect that was imported into Taiwan during the KMT retreat and rule). The suppression worked quite well in both places, where Mandarin has since displaced regional dialects for most matters of life. In recent years, Taiwan has made lots of efforts to bring back Hokkien to distinguish itself from the mainland, but this is actually a fairly recent development...
- Ceremonies at temples: This fell out of favor mostly because Communist parties everywhere have been progressive for the most part of history and like most progressive parties everywhere tended to de-emphasize religion. While most past leaders of the CCP stuck with this, Xi has actually moved the CCP to become much more _conservative_ (reinstating a lot of religious/traditional holidays in place of western ones) so I actually wouldn't be surprised at all if at some point Xi did start to re-introduce Confucian ceremonies as a part of a revival of a more conservative form of nationalism.