It really depends on what kind of production area you're talking about but I'm going to assume a low risk area in which all product is wrapped.
The answer I give depends a lot on how the baskets have been stored but if it's the kind of baskets they use for bread in the UK, they are notorious for becoming harbourage for pests.
This is the kind of thing I'm talking about:

Even if you don't store them outside, your customer almost certainly does. And these are perfect little houses (when stacked) for mice to nest in. Yay!
So whatever you do, when you take them back into a production area, you need to destack them and (very much) ideally clean them (and do all this in an area which is enclosed BEFORE taking them into your production area.) Apart from mice, I've had mouldy (formerly) chilled products turn up in these, often including allergens.
Whether or not they can go through a changing room? It probably isn't ideal but I can't think of a sensible food safety reason not to as long as they're not going on the floor. Strangely enough doing it that way may then reduce the risk (at least) of them being taken in without destacking.
If we're talking high care / high risk then you need to be putting them through an automated tray washer to get them back in which you've validated as effective against pathogens and significantly reducing micro loading and even then it wouldn't be ideal if you could avoid it.
But let me know if I've got the wrong end of the stick!