Yes. many protestors were unfair to the reurning veterans, many of whom where drafted and didn't really want to be there.
Yes they did. To really answer the question, lets look at who said that. Although millions of people across the USA were against the war, not all of them took part in the demonstrations and even those that did, not all of those people resorted to violence and name calling. But, some more radical protestors did resort to calling returning veterans names, including baby killers.
They did that because they perceived the veterans as wantonly killing innocent civilians, including babies. In actuality, most combat veterans took exceptional care when fighting around civilians not to injure or kill them. This caution sometimes led to injuries and death to themselves. However, the media and the photographers that witnessed the death and destruction of civilians and wrote about it, inflamed the anti war groups back in the US. Rightly or wrongly, they made the deaths of civilians more numerous than they actually were.
And of course, the real cases of American war atrocities like the MyLai Massacre, only helped to insure that more and more people back in the states believed that all veterans were baby killers.