People wo say Palestinians didn't exist until 1960 are rewriting history. There was a place called Palestine - referenced by Hansard early 20th century and Trove newspaper archive in the 19th century. People who were born and lived in Palestine in the 1880s were Palestinians - it is derived. It doesn't infer a religion. If you people who were born in Wales are Welsh it doesn't infer they are methodist or CofE.
Palestine 1820s:
https://trove.nla.gov.au/search/category/newspapers?keyword=%22palestine%22&l-decade=182
Poem in 1803 (Palestine)
https://en.wikipedia.org/wiki/Palestine_(poem)
The Palestine Post (later renamed The Jerusalem Post) was an influential English-language newspaper published in British Mandate Palestine from 1932 to 1950.