I have been enjoying breakfast 1-2 times a week. They have multiple griddles so cross-contamination is minimized. While I wouldn't say they are Celiac friendly, they understand and accommodate my request for not only 'no bread' but to not use the same tools with my food as they use to toast buns on the griddle. I order the home-style breakfast. Eggs, bacon and shredded hash browns, no bread.
Steak 'n Shake is a bit of a challenge, but depending upon your sensitivity, here are a few suggestions: cottage cheese, fries, cheese fries, burgers without the bun, shakes, salads, and sodas. Their breakfast menu is also good if you stick to eggs, potatoes, bacon, sausage, etc.
I LOVE this restaurant!!! Why? Cuz *unlike* McDonald's, the fries at Steak N Shake *are* gluten-free!!!!!!!!!!! I take off the bun of their steakburgers, and eat them too; NO fillers in the hamburger patties. Also, because I eat low-FODMAP, knowing there are no onions, garlic, or other spices added to the meat that would cause problems...is huge!! They don't have fillers and junk used in their meat; a rarity in chain restaurants nowadays. I'm seeing no problems from eating their burgers without a bun....so I eat their fries with their burgers (bunless).....and it's awesome food!!! Highly recommended.