In a New York Times Magazine essay, Matt Bai suggests that Democrats and Republicans are equally guilty of scorning dissent:
Such an acknowledgment of common purpose has all but vanished, as the realignment in American politics — a hardening of regional loyalties that began with battles over civil rights and Vietnam — deepened the cultural divisions in Washington. Each party has demonized the other and embraced the notion that dissent can have no moral or intellectual value.
While some Democrats have certainly criticized or undermined dissent, I'm not aware of any evidence comparable to the pattern of vicious attacks on dissent by Republicans between the 9/11 terrorist attacks and the end of George W. Bush's time in office. This is a classic example of false equivalence.