Do the doors lead from the retail space to the outside? Or do they lead from the retail space to the stockroom? Or, indeed, from the stockroom to the outside?
It makes a difference as the doors may be required as fire doors if they are between the retail space and the stockroom.
The door is obviously required for means of escape as it has a push bar fitted.
I don't think there's going to be an easy answer to this because it would be highly unlikely to be acceptable to have these plastic doors obstructing the push bar (and the door opening itself).
I'll tell you what I've seen work once or twice, but you'd have to be very careful about how you arranged it and talk to your fire risk assessor (might even get advice from the local fire service, depending on where you live). If you fit swing free devices to the doors the wrong way round, they can be used to power open (inwards) the plastic doors on actuation of the alarm (normally they're arranged to close doors when the alarm goes off).
If done correctly, people would then have free access to the push bar and to the door opening without having to negotiate past the plastic doors.
If you want to know more about swing free devices, just ask.
If anyone else has got a view on this I'd be interested.
Stu