What is the cause of the hostility between Russia and the Baltic states?
It's nothing the Baltic states did. They were caught between a paranoid and a land-hungry bully.
The Baltic states had the misfortune to be caught between two of the largest belligerents of WWII, the Soviet Union and Germany. In an attempt to buy time, in August 1939 the USSR and Germany signed the Molotov–Ribbentrop Pact to split up Eastern Europe into spheres of influence giving each side a buffer zone against the other. Shortly after they signed the German-Soviet Frontier Treaty to make some modifications.
The Germans wanted Lebensraum. The Soviets wanted a buffer zone against the inevitable German invasion. The Baltic states wanted to retain their independence.
The Soviets didn't believe the Baltic states would be able to resist a German invasion, or thought they'd ally with the Germans. The Baltic states didn't believe their independence would survive a military pact with the Soviets. Unfortunately, that was all true.
Shortly after the invasion of Poland, the Soviets accused the Baltics of not actually being neutral and demanded they sign "Mutual Assistance Treaties" (Estonia, Latvia, Lithuania) which theoretically protected the Baltic states, but just allowed the Soviets to establish military bases on Baltic soil which they would then use in June 1940 to take over those countries.
They tried the same thing with Finland fearing the Finns would either ally with Germany or the Germans would simply bowl them over as they did other neutral countries. Not being boxed in, and assuming the Swedes and Western Allies would come to their aid, the Finns politely rejected the offer recognizing it would lead to the loss of their sovereignty. The Soviets, suspecting Finland had already allied with Germany, trumped up a bunch of charges and invaded in winter of 1939 starting the disastrous Russo-Finnish Winter War.
The humiliating defeat for the Finns led to them becoming co-belligerents (not really allies, just fighting against the same enemy) with the Germans to recapture territory lost in the Winter War, exactly what the Soviets feared. This was known as the Continuation War.
In the end, only Finland kept their sovereignty.