I'm still wondering if a glass-based, non-plastic variant of AeroPress will show up any time soon.
edit: It should also be mentioned, since AP is a relatively unconventional approach to coffee prep, it has evolved over time that many prefer to brew in the AP at significantly lower temperatures than other methods. AP instructions even suggest a 176F brew temperature, which when followed makes it more challenging to get bitter overextractions, when grind size and brew time are maintained. Consistency is a major attribute to AP.
LDPE is cheap and flexible so is really common, especially for things like packaging. It also deforms near the boiling point of water. If you've had a bad experience like a plastic container melting in the dishwasher, or a soda bottle shriveling when filled with hot water, it was probably LDPE.
But there are other plastics like HDPE and polypropylene which are perfectly fine at 100°C. If you're using a plastic product designed for use with hot liquids (like nalgene or aeropress) it will be made of these materials.
I still felt nervous the first few times putting boiling water into a nalgene bottle...
I suspect that the stirring stick, filter cap, and funnel are made of HDPE.