Hi Op, I haven't read all the comments so sorry if I repeat anything but my daughter is autistic and I also run a support group for families with autistic girls - so I meet a lot of children who are autistic!
This is common - but that does not mean you ahve to tolerate it or allow it.
My daughter can get like this - and yes I'm sure it's natural part of a very anxious personality type, often without enough friends and a lot of feeling of low self esteem that they then take out on those near to them - and I think mum is often the one they feel most able to lash out at!
I would be very very clear with her that 'feelings' are tolerated, rude bheaviuor is not. If she is rude to you - you walk away, you don't allow it - it is not doing her any favours to let her speak to you like shit let's be honest.
I think it's a very specific trait to anxious autistic teens but - I really think we have to set the boundary we would want them to set - tell her you won't allow anyone to speak to her like this and you are also not going to allow her to talk to you like that.
She can go away, calm down and return when she can speak politely
if there are really deep issues she wants to talk through (and I know autistic teens have a lot of black /white thinking problems and can get very fixated) maybe it would be worht some family therapy together.
don't let her make you a punching bag.