From Origins A Short Etymological Dictionary of Modern English, Eric Partridge:

Palestine, whence Palestinian

The adj derives from L Palestinus (var of Palaestinus), adj of Palestina, var of Palaestina, trin of Gr Palaistine, itself from H Pelesheth. The inhabitants were, in H, Pelistim or Pelishtim (cf Ar Filastin), whence Gr Philistinoi, LL Philistini, both pl, whence, by b/f, the F sing Philistin, whence E Philistine (n, hence adj). Strictly, the Philistines inhabited SW Palestine; "after harassing the Israelites for centuries they were finally assimilated by the native Semites" (Webster) and were regarded as barbarians, hence Philistine, an unenlightened person, hostile to art, literature, thought, the transition being aided, both in E and in F, by G Philister, a G universities' (orig, theological students') slang name -- at Jena as early as C17 -- for a townsman, hence outsider, hence any ignorant person. First used in France by Theophile Gautier in 1847 (B & W), Philistine was "introduced into England by Matthew Arnold (cf Judges, xvi, 9)" (Walshe). Hence Philistinism.