Complex sentence: She was Jewish in a climate of Soviet anti-Zionist campaigns, her family had been purged during the Stalinist era and her personality was defiant, so she was not allowed to tour outside the country for sixteen years after joining the Bolshoi.
Split into simpler sentences: She was Jewish in a climate of Soviet anti-Zionist campaigns. As a result, she was not allowed to tour outside the country for sixteen years after she had become a member of the Bolshoi.