I understand the prospect of hating labels but it is simply false to say that different types of players don't exist within the Smash verse. There ARE players who value competitive performance, and there are players who do not, I don't see how it's offensive to either camp to differentiate between the two.
I think the problem isn't the label, but the usage here. If you use the label yourself, it's an identification, but if someone else is using it, it's a way to show exclusion. There's obviously a HUGE difference between:
"Oh. I don't follow most of the advanced technique stuff. I'm just a casual player"
and
"Of course, you wouldn't like this. You're just a casual player."
Similarly, the two labels, as have been shown aren't necessarily mutually exclusive or even fully inclusive of either. I actually wouldn't consider myself either a casual or competitive player. Game playing has kinda become a form of artistic expression for me over the years. I like to play games in unusual and new ways, not necessarily optimal ways. This often requires a lot of skill and practice, but I'm not exactly doing it in the name of competition.