Can you mount a plastic junction box to metal studs?
You usually see wood framing with plastic electrical boxes and nonmetallic cable in residential construction, and metal framing with metal boxes in commercial construction.  However there's nothing that specifically prohibits the combination of metal framing and plastic boxes.
NEC* article 314.23(B) addresses how boxes are mounted, and there's nothing in there that would prohibit you from mounting a plastic box to a metal stud.

B)  Structural Mounting.  An enclosure supported from a structural  member  of  a  building  or  from  grade  shall  be rigidly supported either directly or by using a metal, poly-meric, or wood brace.
(1)  Nails  and  Screws.  Nails  and  screws,  where  used  as  a fastening  means,  shall  be  attached  by  using  brackets  on  the outside of the enclosure, or they shall pass through the interior within  6  mm  (1⁄4in.)  of  the  back  or  ends  of  the  enclosure.  Screws shall not be permitted to pass through the box unless exposed  threads  in  the  box  are  protected  using  approved means to avoid abrasion of conductor insulation.

There are NEC rules restricting the use of armored cable with plastic boxes, but if you are using nonmetallic cable (type NM B, such as Romex) and following the NEC rules for running NM in metal framing, that could be compliant.
Like other electrical equipment / materials, the box has to be used according to its listing - that is, you have to follow the manufacturer's instructions, specifications, and restrictions - and the listing may restrict the use of the plastic box in certain fire rated walls, etc.  But that's not necessarily going to rule out plastic boxes with metal framing.
*The National Electrical Code (NEC) applies to most electrical installations in the US.