You should be able to wash acrylic paint with no problems since it's no longer water soluble when it's dry, especially after it's completely cured
(not just dry ...say a week at most). Dryers should be okay too. In fact, all those fabric paints you see are just acrylic paints with mediums added to make them apply more smoothly and thinly, etc.
As for the polymer clay part, there's no problem with washing and drying most solid polymer buttons either (do not dry clean
There is a problem though with the brand
of polymer clay you'd be using, and that could be a deal breaker.
Sculpey, SuperSculpey and Sculpey III are all brittle after baking, and can break or chip with stress ...this is true mostly for any Sculpey items which are thin or have projecting parts.
So if you made buttons with those 3 Sculpeys which were very
thick and rounded, or even more like balls than flat, there would probably be no problem... or if you hand washed and hung dry, you could avoid most of the stress during washing and drying.
That wouldn't avoid the stress caused by wearing the item though, or the stress on the holes from the thread. It's possible that a couple of layers of acrylic paint could make the Sculpey strong enough... you'd just have to find out.
There is no problem at all with making polymer buttons though if you use other brands of clay.... like Premo, FimoClassic (but not FimoSoft
...it's now like Sculpey III), Kato Polyclay and Cernit are all strong clays after baking.
In fact, you could mix your Sculpey with one of those and make it stronger depending on how much you add. Buttons are so small though that you'd probably be better off just buying one of the stronger clays to use for the buttons... you could get quite a few buttons from one small package of any of those brands for about $2.00-2.50 (unless you happen upon a sale at Michaels!).
I have a whole page at my site on making polymer clay buttons, if you're interested in checking it out:http://www.glassattic.com/polymer/buttons.htm
GlassAttic ...polymer clay "encyclopedia"http://glassattic.com/polymer/contents.htmfor the upcoming all-polymer clay board here at craftster, check here!http://www.craftster.org/forum/index.php?topic=72141.msg813624#msg813624