It is part of the reason D&D 4e sucked so hard, and why D&D 5th isn't much better. It is why you don't see this problem nearly as much in systems like Mutants and Masterminds or Champions. Why? Because in M&M or Champions, literally everything is possible, though it may take work with the DM to translate some things. Sure, I can do an M&M character that has, say, Cold Control powers, with fighting skills and appropriate gear. That's easy. I can also easily do someone with the ability of Nacho Cheese Control, and make them able to do crazy shit with that. And because I spent an hour making the character just to say I can, I have it out of my system, and play the cold controller in games.
See, sometimes people get an idea in their head, and if they aren't able to work that idea into something playable, then it is going to bug them constantly until they get it out of their system. Which means they're going to bug their DM about it, or keep suggesting it here, or other places. Sure, the idea might be as stupid as Nacho Cheese Control. But once it is out of their system, they'll be able to consider more 'normal' concepts.
Only just got round to reading this thread but I'm guilty of this to a certain extent, sometimes I get the craving to build a really exotic pc or npc and have been known to spend several days in my books building them and making them work, just because something is a rare occurance in sr does not mean it never appears, on the contrary it makes that time when you do encounter it all the more memorable.
On to the topic of actually playing an extremely rare race etc. If I'm building one of these characters that some people might consider as a "look at me" the first thing I consider is the setting, lets say an anthropomorphic kitsune was a race for example and I had one it's not something I would likley play as a pc in mirrorshades or black trenchcoat groups doing normal runs, but not all games are set like this in fact some games can have situations where this kitsune would fit rather well.
Next is how you play the character, if your just being the attention grabbing special snowflake that thinks it's all about them, yeah it's a problem. If however you are able to get a feel for the character you can add lots of little details that add realism and depth to it without making the game "all about you" in fact it can even encourage other players to flesh out their manorisms, little subconscious habbits and things like that.
Next up is other players recognising the difference between when somone is grabbing attention due to acting like a special snowflake and when somone is the center of attention for other reasons. It sounds obvious right? You would be wrong, I have seen players singled out because the group EXPECTED them to act like a special snowflake so when they briefly became the center of attention
for a completley different reason some members of the group treat the pc like he's a special snowflake from that point on.
This brings me to my final point, I wish people would be more accepting of characters outside the "norm", if I'm playing one like that it's because I really dig the race and unique challenges it can bring and as a result find it enjoyable, not because I want to be the center of attention and the same is true of most of the people I have seen playing them, yes there are special snowflakes out there but for the love of... stop assuming anyone who picks a character that can be played like one IS one, the odds are you are ruining the game for that player just as much as they would be for everyone else and they probably haven't done anything to deserve it.