I do not put anything plastic in the cages ... but, then ... I have allot more to watch out for ... I like the glass or metal dishes, they are much heavier and do tend to stay in place better. I got a good laugh one day when one of the girls that got one of my chins sent me a picture of her glass baking dish with a little cage wire corral attached to the cage with the glass baking dish setting inside of it ... sometimes it takes a person with a great imagination to make things like that ... if it works, and it did ... I thought it was cute.
You could probably do the same thing with wood and bolt it to the cage, then set the dish inside of it. Sorry about making you paranoid.
If you do decide to get plastic ... be very vigilant and remove it at the first sign of tooth marks on it.
Jo Ann