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The spores of some mushrooms almost certainly contain the same toxins as the mushrooms which they come from. So there could be some cross contamination. I am unaware of any actual poisonings from that source. Considering how nasty some mushroom toxins can be it's probably a good idea not to risk it.
Another risk is cross contamination with maggots. They will happily burrow from one mushroom into another. If you're one of those people who ignore 'em, then that's not a problem.
If you get enough mushrooms in one bag then you may find that those on the bottom are crushed. Then you've got damaged mushrooms, and there is also the possibility of cross contamination by squeezed out mushroom juices.
The biggest problem is probably identification. If everything is going into one bag then you don't have any notes on where each one was found (on wood, on the ground, on dung, under what kind of tree, etc). For lots of mushrooms those things are important imformation if you want to accurately identify them.
Try getting some waxed paper bags or brown paper lunch bags. They're cheap and you can put lots of those into your big bag and still keep every collection separate.
Getting back to your initial question - probably not. But there's no easy way to guarantee that. Considering the risks, it's probably not worth taking a chance.