I spotted these banners a short while ago near Zhongxiao Fuxing MRT Station in Taipei. I don't know how long they are displayed up there, but judging by how worn-out the color is on the smaller one on the right, it must be for a long while. The bigger one in Chinese looks newer and I'm very curious about how they managed to put it up there. It says "台灣人不是中國人" ("Taiwanese are not Chinese"). The term "Chinese" is here most likely related to "nationals of the People's Republic of China", not "Chinese" in the ethnic sense, although it can also mean the latter in some cases (read more).
Taiwan, unlike China, guarantees freedom of speech and freedom of expression. The people behind these banners are either very patriotic citizens, or part of the Taiwan independence movement (or Taidu, 臺獨). They are well aware, that if they were living in China right now, this banner would most likely be taken down, the people behind it questioned, and most probably to disappear in one of the numerous labor camps across the country for an unknown period of time. Now you may agree or disagree with the statement on the banners (that depends on your political convictions), nevertheless I am sure that you'll not contest the statement, that freedom of expression and freedom of speech are universal values, that must be cherished and preserved for future generations. Keep in mind, that these freedoms are rather an exception in the region, which makes Taiwan's young and often fragile democracy so much more significant.