A bit of history, in case you aren't sure why the Jewish population of the Ukraine is worried and talking about fleeing.
Some Ukrainians cooperated with the German occupiers, participating in the local administration, in German-supervised auxiliary police, Schutzmannschaft, in the German military, and serving as concentration camp guards. Nationalists in the west of Ukraine were among the most enthusiastic early on, hoping that their efforts would enable them to establish independent state later on. For example, on the eve of Barbarossa as many as four thousand Ukrainians, operating under Wehrmacht orders, sought to cause disruption behind Soviet lines. After the capture of Lviv, an important Ukrainian city, OUN leaders proclaimed a new Ukrainian State on June 30, 1941 and were simultaneously encouraging loyalty to the new regime, in hope that they would be supported by the Germans. Already in 1939, during the German-Polish war, the OUN had been “a faithful German auxiliary”, according to
Professor Ivan Katchanovski of the Davis Center for Russian and Eurasian Studies Harvard University writes that during the war the leadership of OUN B and UPA was heavily engaged in Nazi collaboration - at least 23% of its leaders in Ukraine were in the auxiliary police, Schutzmannschaft Battalion 201 as well as other police formations, 18% took part in training in Nazi Germany's military and intelligence schools in Germany and Nazi-occupied Poland, 11% served the Nachtigall and Roland Battalions, 8% in local administration during the Nazi occupation, and 1% in the SS Galicia Division;according to Katchanovski the percentage of Nazi collaborators among the OUN-B and UPA leadership is likely higher than those numbers, as much data from early occupation is missing
July 1944 saw the Battle of Brody (close to Lviv in Western Ukraine), a clash of arms that was to be the first serious test for the highly controversial SS Galicia division, a branch of the German war machine manned exclusively by Ukrainian volunteers. This SS group was one of a number of international battalions recruited during WWII by the Germans and was seen by nationalist forces at the time as the first step towards creating an independent Ukraine.
The most notorious massacre of Jews in Ukraine was at the Babi Yar ravine outside Kiev, where 33,771 Jews were killed in a single operation on September 29–30, 1941. (An amalgamation of 100,000 to 150,000 Ukrainian and other Soviet citizens were also killed in the following weeks). The mass killing of Jews in Kiev was decided on by the military governor Major-General Friedrich Eberhardt, the Police Commander for Army Group South (SS-Obergruppenführer Friedrich Jeckeln) and the Einsatzgruppe C Commander Otto Rasch. It was carried out by a mixture of SS, SD and Security Police, assisted by the Ukrainian Auxiliary Police.
Professor Alexander Statiev of the Canadian University of Waterloo writes that Ukrainian Auxiliary Police were the major perpetrator of the Holocaust on Soviet territories based on native origins, and those police units participated in the extermination of 150,000 Jews in the area of Volhynia alone. German historian Dieter Pohl in The Shoah in Ukraine writes that the auxiliary police was active during killing operations by the Germans already in the first phases of the German occupation. The auxiliary police registered the Jews, conducted raids and guarded ghettos, loaded convoys to execution sites and cordoned them off. Some 300 auxiliary policemen from Kiev helped organize the massacre in Babi Yar. They also took part in the massacre in Dnipropetrovsk, where the field command noted that the cooperation ran "smoothly in every way". Cases where local commandants ordered murder of Jews using police force are known. In killings of Jews in Kryvy Rih the "entire Ukrainian auxiliary police" was put to use.