You shouldn’t be afraid of plastic parts on your coffee maker; they are not all toxic. Almost all automated coffee makers will have some plastic components. Even if you can’t see any, the chances are that hidden inside plastic is everywhere, from computer circuits to latches and buttons.
However, most of the best coffee machines will state that those plastics do not come in contact with the brewing process (water, coffee grounds, and final brew).
Handles, buttons, and dials are good examples of plastics that might not necessarily be BPA-free. So a coffee maker can have some plastics and still be safe to use.