There are two reasons - and neither are NICE things about your mother - but they are HUMAN things.
Your mother is human and does not have HFA. She does not have the same drives you (or I) do. She cannot understand your passions, especially since they are over something "childish" and "meaningless" like Furbys. She likewise does not understand your need to stimulate yourself by headbanging. She does not have passions like these. She does not feel the need to stimulate herself. Thus her reaction is that she simply does not want to deal with anyone who does these things - they irritate her on every level because they are not normal and they are disruptive of her life. That is why she is intolerant of it.
If she were not your parent, it is likely that she would distance herself from you, or create a situation where she would not have to deal with you. Unfortunately, she IS your parent, and feels responsible for your lack of "normality". So on top of being irritated by the way you act out, she also feels a very strong need to control your acting out. But instead of vocalizing these things, she just gets upset with you, and tries to control your actions and passions by yelling at you.
The reason why she gave you no information about your condition (and why my mother refused flat out to let me get tested) is that she feels like she would be a failure to admit that something was actually "wrong" with her child. Instead of finding out what the issue is and the acceptable methods of teaching and training HFA children, she assumed that your condition was made up - and that ultimately, with her own hard work, she could snap you out of it.
One day, she may come to grips with the fact that she cannot control everything (as my mother did), or she may try to control you forever via her shouting and disapproval (as with my husband's mother).
The reason why she loves your singing, but not your love of furbys is just as simple as her seeing one thing that IS annoying versus one thing that ISN'T. what will hurt her, is if you passion ever shifts (as mine does about every 1-2 years), she will be DEVESTATED that you no longer care about singing anymore and will not understand why you no longer care about it.
But if you love her, just try very hard to understand that to "normal" people, most of us HFAs are the most annoying people on the planet. That's nothing to sob over, but you should keep in mind that if she cannot share your passions that it is not such a bad thing to keep it to yourself or at least moderate the amount of time you spend talking about it. Likewise with the stimming, take it out of the room if you can. Or find other smaller things you can do to stimulate yourself (I used to spin in circles - but I can get a very similar effect from tossing my tied-back hair back and forth).
At any rate - I hope this helps a little. And don't be angry at your mother - you're just out of her helm of understanding at the moment and as soon as she comes to grips with it, she'll be far more pleasant to deal with.