In the early 20th century it was effectively split between Polish, Jewish, and Ukrainian. Was this demographic divide consistent with eastern Galicia of 1600? I'm assuming the number of Jews and Poles was far higher in the 20th century? Why did they move to this area?
To say that Galicia was inhabited by Poles, Ukrainians and Jews would be a significant understatement of the cultural diversity of that region and eastern parts of Poland and Polish-Lithuanian Commonwealth prior to 1772 when the first Partition happened. The country as such, being located in the dead centre of Europe and being the second-largest European country after Russia naturally included different ethnic and cultural group and the central location facilitated intensive movements, both peaceful, as trade and migrations and hostile, such as wars and pillaging raids. Until early 15th century, the inhabitants of the Kingdom of Poland were mostly Poles or polonized Western Ruthenians, with significant influx of Jews and Germans after the unification of Poland under Władysław I and rapid development during the reign of his son, Kazimierz III (what I recently summarized here), the union with Grand Duchy Lithuania in 1385 that led to the formal real union in 1569 meant that the Poles were joined by a similar number of Lithuanians who, for the most part, were Ruthenians and Western Russians who joined the Lithuanians in the wake of the Mongol invasion and significant weakening of Kievan Rus. Now, in early 15th century, Poland and Lithuania entered the war with Teutonic Order supported by Holy Roman Empire and Papacy, so Polish king Władysław II and Grand Duke or Lithuania Vytautas decided to invite Wallachian nobility (mostly ethnic Romanians and Hungarians) to join them in exchange for the lands located in vast yet sparsely populated southeastern Poland (Lesser Poland) and southern Lithuania (Halicz-Wlodimir province) as this decision was opportune for the invited nobles and facilitated country development for Polish and Lithuanian rulers. Now, in the 16th century, this already diverse country was joined by Karaims (Turkic Jews who moved north from Crimea and Seljuk regions), Armenians (most commonly merchants operating the local stage of the Silk Road) and Mongols (mercenaries and defectors from the Crimean Khanate), creating a very complex patchwork of cultures, ethnicities and religions. It is generally accepted that the religious tolerance typical for the Polish-Lithuanian Commonwealth in 16th and 17th century and highly unusual anywhere else in Europe was a result of the long traditions of co-existence between different confessions, started with the aforementioned Union of Krewo, where predominantly Catholic Poles were joined by primarily Eastern Orthodox Lithuanians and large influx of Jews who, being expelled from various countries in Western Europe, were welcomed and enjoyed protection of the Polish rulers.
Now, a side note concerning Ukraine. The 'Ukrainian' nationality is a relatively new phenomenon, formed in the second half of 19th century in the wake of the general rise of nationalist sentiments accross Europe, although Ruthenian inhabitants of South-Eastern Polish-Lithuanian Commonwealth were attempting to form their regional identity centered around that of Zaporozhian Cossacks at least since the first haf of 17th century. Given the specific organizational and cultural traits of Cossacks and opposition to the Polish and Lithuanian regulations that would rather see Cossacks simply as common peasants, we can consider Cossacks a separate culture that reinforced Ukrainian attempts to achieve independence from both Poland and Russia in 19th and 20th century.
As we can see, the Eastern Poland and Lithuania was a very diverse region and although the government changed rather drastically after the three Partitions in 1772, 1793 and 1795 that eventually led to a total dissolution of the Polish-Lithuanian Commonwealth, the ethnic and religious diversity largely remained intact, with an additional influx of native Russians e.g. taking administrative positions in what was essentially a province of the Russian Empire. As the Ukrainian Ruthenians, Poles and Jews formed the largest ethnic groups in the area, they also quickly grew, becoming the dominant groups in the beginning of the 20th century.