What impact, if any, did Senator Joseph McCarthy have on the exercise of free speech?

Joseph McCarthy called free speech into question on multiple occasions. Namely, with his push to create the House Committee on Un-American Activities(HUAC). The HUAC was created to investigate organizations or even individuals suspected of having communist ties. This was in light of the second Red Scare, when communism was a big fear among the American people. Because of this, free speech, at least in the case of communism, was somewhat dismissed. Joseph McCarthy only added fuel to the fire with his fear mongering.

Explanation:

to keep us neatruel and not get involved in any wars

he assumed control of treaty negotiations with a hostile power