Hi and welcome to the community, @Brian_LeBleu!
You can cut rubber‑stamp material on the iEngrave — just make sure it’s specifically labeled “laser‑safe.” Most rubber‑like materials will release toxic fumes when hit with a 10W diode laser, so you’ll want a proper extraction setup in your workspace, just like @Cory_Barger mentioned earlier.
One of our members also tested cutting EVA foam on the iEngraver, and you can check out their results here for reference:
Cutting and Engraving Tests on Different Materials (Part Two)
Hope this points you in the right direction! 
Thank you @Samantha_Bryant and @Cory_Barger for tagging me on this topic.