I started researching this on the net and it seems that there are a ton of contradictory opinions out there. Here is what I have found so far:
As a general rule, if the bobbin case is metal then use metal bobbins.
As a general rule, if a machine is sold with plastic bobbins then use only plastic bobbins in it.
Older vintage machines came with metal bobbins, but plastic bobbins work in them. The only thing is that switching between the two can cause changes in tension.
Metal bobbins of the same class can be of different qualities. Vintage metal bobbins were machined accurately, but some of the modern metal bobbins are not machined as well and can cause problems in some machines.
Finally, I found this which seems to actually directly address the original question:
"10 pack of plastic class 15 bobbins fit all class 15 drop-in rotary or oscillating hook machines, whether older front load or newer top drop in class 15 bobbins. It is ok to use plastic bobbins in metal and plastic bobbin cases. Metal class 15 bobbins should only be used in front load metal bobbin cases as it may cause undue wear on top load plastic bobbin cases, but will work fine."