The thing is Smash got big enough, early enough that it didn't need the FGC, so it developed its own culture which is separate from the FGC. Add to that being on a Nintendo console and you get a situation where there is very little overlap between the communities.
It's not jut that, though. There's always been this misconception from the Smash side because of the very vocal minority of the FGC saying stuff like, "ooh smash is bad" or "smash isn't a real fighting game" or "smash is blah blah blah" etc. painting the people who play it as outcasts. And what I'm saying about that is long before the FGC got really big.
Now that it's really big and figureheads are being made because of twitch streaming you can now know who matters when it comes to what they're saying. The people who say all those things aren't speaking for someone like UltraDavid or Justin Wong like people would think way back when.
The more you keep thinking the communities can't come together, the more likely it is they won't. If you give them the right push and support it, it'll all come together just fine.