Question

How were Sacco and Vanzetti linked to the fear of Bolshevism and anarchism?

Answer 1

They were Italian immigrants--following WWI, immigrants in particular from warring countries were seen as dangerous and often target as trying to destroy America. 

Sacco and Vanzetti were Italian immigrants and anarchists accused of a murder in their local neighborhood. Their link to an immigrant group and known union activities led to their arrest and execution. The US entered a time of "normalcy" and wished to rid the US of foreign influence to include anarchists and Communists. 

Answer 2

What they were involved of was robbing a shoe corporation at gunpoint. Nothing to do with anarchism. But at the claim, their political connections kept coming up as reason quite to declare them derelict. Apparently, the judge actually said to the board at one point, "This man [Vanzetti], although he may not have actually performed the crime attributed to him, is nevertheless morally culpable, because he is the enemy of our existing institutions."