My wife is Taiwanese, so I can confirm Taiwanese and Chinese get along fine. Many marriages, friendships and business partnerships cross the Taiwan Strait.
However Taiwanese people don't use their passport to travel to China. China doesn't recognise it. They are issued a travel permit by the PRC, similar to citizens of Hong Kong and Macau.
Not only that. You can’t just travel from China to Taiwan. It’s a bit difficult. Most people must travel as part of a tour group. Unless it’s business or you have family to sponsor you or something like that. Basically you can’t just jump on a plane and have a holiday in Taiwan from China.
When president President Tsai Ing-wen was elected it became difficult. In both 2016 and again in 2019. China banned solo travel from certain cities in China to Taiwan.
I was just talking to someone who came back from working in Shanghai and that’s not what she told me but it’s very possible she misunderstood my question.
ROC and PROC don't recognize each others' passports, since both states hold the official position that the other state does not exist (and that travelling between the mainland and Taiwan does not, therefore, count as "international travel").
However Taiwanese people don't use their passport to travel to China. China doesn't recognise it. They are issued a travel permit by the PRC, similar to citizens of Hong Kong and Macau.