Another option is to buy toaster bags. Then you can still use the same toaster but the bag will keep your bread safe from contamination. I've never seen them in a store but you should be able to buy them online.
It seems they are available everywhere in the UK but not in the USA.
Here's a USA news video about Tosta Bags in this example it's making grilled cheese in the toaster,
but as you can see it would be excellent for Gluten Free bread in a shared toaster.