I prefer to take the risk. There's nothing wrong of carrying reusable shopping bags. For sure it will not be confiscated if you will pack it nicely and put in your luggage. To be sure, better check your airlines.
I would think that the reusable canvas shopping bags wouild be fine in you luggage or your carry on. I wonder what the deal is with no plastic bags though. Are they afraid passengers will start suffocating people?
I don't see why they wouldn't be allowed in carry on luggage or your other luggage either. I am curious about why they wouldn't allow plastic bags also? How are they a danger?
I suppose that, if the plastic bag were big enough, it could be used to suffocate someone. That's about the only way I can think of that a plastic bag might be harmful. Unless, of course, plastic bags can be used in making a bomb.