Never Tell An Autistic to Have "Quiet Hands"

Just don't do it.
It's a bad idea.
It sounds simple enough - I guess I can see where the confusion comes from - but it's really important for people to understand that when autistics flap or shake or wave their arms, they are doing so because it is a technique that allows us to better understand the world.
Stimming is difficult to describe to a neurotypical person.  Autistics of all creeds understand stimming; it's one of the things that connects us all together.  But to neurotypical culture, it is deemed "weird."  It's just not something that NTs do.  And, since autistics and NTs live together in this beautiful world, sometimes we have to make concessions for one another.
But, as a public service announcement to neurotypicals everywhere, please know: we stim because we have to.  Stimming is not a choice; in fact, stimming is a reflex for most autistics.  Stimming is not always seen as acceptable among neurotypicals, and we are aware of that.  Sometimes, we are self-conscious.  We don't like it when you judge us.  But even though we're afraid of what you'll think when you see us stimming, we cannot stop.  Stimming is just something we do.
I should clarify here that not all autistics stim, and sometimes our stims take different forms.  Some autistics have vocal stims.  Others have physical stims.  Some of us - including myself - have a combination of both.
In my case, I stim more when I am nervous or anxious.  I will repeat words - words that I like because they sound nice, not words that are relevant - and shake my hands or flap my arms.  I hate stimming in public because I'm always afraid that I will be judged.  I never used to notice and I especially never used to care, but now I am afraid and it is very difficult for me to stop stimming once I get to this heightened state of anxiety.
I've never been told to quiet my hands, but it has happened to other autistics I know, and it seems very impolite to me.  I would get more nervous if told to quiet my hands.  I would probably stim more.  And, honestly, being told to quiet my hands might even cause me to melt down.
My point here: be tolerant.
If you are neurotypical, you cannot understand the mind of an autistic, no matter how hard you try.  We are different than you.  It's OK to admit that.  But it's not OK to refuse to accept that we are also of value.  We do things differently.  And that is OK.  This world is full of all different and unique  individuals and it is important to remember that we all must coexist together.  Please be tolerant of neurodiversity.