What is the context of this assertion which we see continually on this forum? Because having a personal (as opposed to a political) opposition to abortion does not a social conservative make. (I assume this is the basis on which this claim is made; something which blissfully ignores the fact that even Ted Kennedy held the same position.) If that makes a social conservative, then I am a social conservative. Most people on the forum probably are. This is not a very convincing position.
Kennedy died before the whole social debate, not just in the Democrats but in America, progressed in the 70's after, eg, Roe etc. As such, locating him as a social conservative on today's spectrum is an excercise in epic pointlessness. You may as well say that LBJ or FDR was a social conservative. Shit, by this kind of thinking, William Jennings Bryan was one of the most socially conservative politicians in American history. A totally limited, anachronistic, and silly analysis.
In other words, a mainstream Democrat?
The problem with this question is that so many people on this forum on both sides of the spectrum insist on viewing 'real' Democrats as left-wing, when in fact this is a nonsense. I don't see anything which substantially differentiates Kennedy from - say - Carter in policy terms. Centrist Democrats are not some kind of factional clique, they are, both in historical and contemporary terms, one of, if not the main bodies of the party.
Here is where I disagree: If you read Evan Thomas's biography of RFK, you learn very quickly he was extremely religious and a staunch moralist. He was also a homophobe, though that was more a general discomfort than any sort of anger. So I don't know for sure if Kennedy was a social conservative. However one could easily see him as one.
On economic issues, yes he would be a mainstream Democrat in today's party. But if you read the party platform of 1976 you see a very liberal party indeed. They wanted to keep price control in place and dramatically expand the size of government. Carter didn't follow this plan, and was the first New Democrat elected President. Clinton followed his mold and really brought the party into the 21st Century. Obama has stayed on that track. So yes, he was a mainstream Democrat in today's world on many issues, but more socially conservative than most.