Anne Frank was not right in thinking that the Jews were to blame for the war. She was a victim of Hitler's insanity. The notion that a pure race of "supermen" would be bred from pure "Ayrian" people of Germanic race is what led to the rounding up of Jewish people and others to be either killed outright or to be worked to death in slave labor camps.
Anne's thinking is something that sometimes happens to victims in that they come to believe that their aggressor is correct and that they deserve the punishment that is inflicted upon them. The victim is cut off from all outside communication and therefore only subject to the thinking of the agressor. Because of their hiding and living conditions, a kind of "camp mentality" developed in the Frank's household group.
Anne's family and many other Jewish families had done nothing but live quiet lives and work for a living just like their non-Jewish neighbors for many years. Then the Nazis took over, and Germany became intolerable.