I mix it up. I use paper, plastic, and sometimes glassine envelopes. Plastic is often cheapest and the easy opening is convenient, but paper seems better for packaging recently harvested seeds even if they appear adequately dried. Glassine combines the best of both but is usually the most expensive option. Homemade origami envelopes are fine too.
If a host requires plastic that's fine but I have opted not to join a swap or two because of that requirement. Seeds around here are often cured and packed as they become available so that there is time to join several swaps without a scramble to get them sorted and packed at the last minute.
