Been mushroom hunting for over 30 years. And you can definitely use plastic bags, just don't leave them in the car for long and when you get home, put them in a basket in refrigerator. Nothing wrong with plastic bags when going mushroom hunting.
An individual mushroom produces millions of spores, but in a stable population, on average only one spore produces another mature mushroom. I'd be very surprised if mushroom populations are limited by the dispersal of spores.
I can't speak to whether or not plastic bags completely prevents spores from falling to the ground, but I agree with lumberingjack's sentiment about using a mesh bag to increase the odds of successful propagation. Mushrooms continue to drop spores even after they are picked. Taking spore prints of harvested mushrooms is one way enthusiasts create strains of their own.
[0] - https://radicalmycology.com/educational-tools/mushrooms-101/...
It's forbidden by law in Europe simply because it will prevent the spores to drop.
Use a wooden basket instead.
However in Italy, for instance, the Legge 352/1993[1] says explicitly to use proper "containers" in order to favour the spores' spreading.
That's a generic normative then local authorities could rule other details on harvesting and selling them.
- [1] http://www.salute.gov.it/imgs/C_17_normativa_1787_allegato.p...