I think you might be confusing the laser with the shop bot. One of several types of the materials you can’t cut on the laser(s) are anything containing chlorine.
As far as the shop bot goes there are several issues to contend with. Spindle speed. The lower end speed of the router is 10000-12000 rpm (from memory i think). This will limit the material/end mills you can use. The dust collection might be an issue. The last time I was in the dust boot was gone, so it was not collecting the cuttings on the shop bot well.
I have cut foam/wood I would not see an issue with plastics. You will need to pick the correct bits and feeds and speeds to not damage the work or bit. Wood will char plastic will melt. The foam and many plastics will have a static charge and the dust/pieces stick to everything, so they need to be cleaned well.
You might also want to pick up an end mill made for the type of plastic you are going to cut, and use it only for that. Then you would have the best outcome.
As long as the speeds are correct and you are making chips and not fine dust, and the dust collection is working properly the shop bot wont mind.