In this context, shape means to influence or impact. When something shapes current debates about individual rights and freedoms in America it means it has played a significant role in forming or molding those debates.
Related terms
Influence: The power or effect that something or someone has on shaping opinions or decisions.
Impact: The significant effect or consequence that something has on shaping events or outcomes.
Mold: To form or shape something according to a particular pattern or idea.