First, even if antiwar speech does give aid and comfort to our nation's enemies, the First Amendment limits treason prosecutions as much as it limits sedition prosecutions or hate speech prosecutions. There are always some people, whether in the government or in editorial offices, who are willing to assume the worst about the intentions of those with whom they disagree. But we the voters are entitled to hear the views of those who oppose the war (for whatever reason) as much as the views of those who support it.
But more importantly, the response to the Sun's pragmatic claim is that the First Amendment is a profoundly pragmatic protection. It is justified by the natural tendencies of governments and their allies — tendencies that are only exacerbated in wartime — to assume that they're right, and that their opponents are traitors.
Sometimes, though, the government is wrong — and the only way that we Americans can tell whether the government is wrong is by hearing the arguments on both sides, before the war and during the war. Free speech has persuaded the Sun's editorial board (as it has me) that war is right. But I'm confident in my position precisely because I know that the war's opponents were free to present their best arguments against it. Likewise, to be confident that the government will fight the war the right way, and will end it at the right time, the public needs the freedom to hear the government's critics as well as its supporters. The same First Amendment that protects the Sun and the National Review protects the war's critics as well.