Can you suggest any Carb Free thickeners that don't affect the flavour of soups/casseroles?
Xanthan gum and methylcellulose both are used in such small amounts that any carbohydrates in them would be of miniscule quantity.
For casseroles I would recommend making sauces that are thickened with eggs -- savory custards if you will. Soups can easily be thickened with pureed cooked vegetables. Yes, this will add some carbs depending on the veggies used, but the amount of fiber in relation to the carbs negates some of the effect. Stay away from very starchy or sweet veggies, like potatoes and onions, and limit the use of carrots/beets. For some soups pureed cooked legumes (ex. dried peas, lentils, or beans/soybeans) would work well.
Some carbohydate-based thickeners work better than others. Cornstarch is more effective than flour, for example, and you might have even better luck with tapioca starch or potato starch.
Otherwise, I like the egg idea, although that'll add a bit of flavor, and it's hard to do without getting an egg-drop effect. Or, letsee... okra will thicken your soup!