Can I mix acrylic paint into liquid latex rubber?
Acrylic paints, or modified acrylic paints, are often used to color latex, but not for what you want to do.
Latex is a little finicky.  Many colorants will cause it to do unwanted things, like coagulate quickly into a sticky, gloppy mess, fail to dry properly, or change its characteristics.  There are colorants designed specifically for latex.  My understanding is that some of these are acrylic-based (basically a suspension of acrylic paint in latex with additives like ammonia to control coagulation).  Some people do add acrylic paint to latex, often diluting it with a little ammonia.
A big exception to acrylic paints is metallic paints, which is your objective.  Many of these cause the latex to coagulate.  You would need to test the specific paint.
As a general rule, it's usually easier to color latex with pigments than liquid colorants.  Also as a general rule, you don't want to adulterate the latex with too much of anything.  The latex is mostly water.  When it dries, there's much less volume of rubber.  So the colorant will represent a much bigger proportion of the rubber mixture, and have a big effect on its characteristics.  It usually isn't a good idea to add more than about 5% colorant.  Fortunately, it doesn't take much colorant.