Having recently started a low carbohydrate diet, I have started to think about what one does for us folks and diabetics at a tea party. Tea and cream are perfect and need no change. I have successfully made 2 batches of scones using low carb ingredients - special flours and sweeteners (I use a Splenda type sweetener that has fiber in it and brings the calorie and carb count for sweetening to zero) that have turned out very nicely, with very little loss of flavor, although the texture is a wee bit different. Stuffed mushrooms, pates, different kinds of deviled eggs, custards, soups without pasta all come to mind. You can make cookies and crusts from finely ground nuts. I haven't tried a cake yet, however.
There are low carb items like tortillas, pita bread and bars available in some grocery stores, certainly at Walmart. There is even halfway decent ice cream, called Carb Smart by Breyers that some grocers have. Fresh berries with whipped cream are excellent desserts. If you want to consider doing this for a friend(s) for a tea, Dana Carpender has authored an excellent cookbook, 500 Low Carb Recipes, that I know many libraries have or can order for you. There are many diabetic cookbooks that have very good recipes in them. If you want to make things requiring more specialized items, check a health food store or got to www.netrition.com online (which is where I get special flour)and click on low carb. One of the good things about them is they ship anything anywhere in the continental US for only $4.95.
There are also many people with gluten problems that would make a standard tea difficult if not impossible. Again, there is much on line and in libraries to help with this. There are also currently many, many mixes available at health food sores, Walmart and grocery stores to make really good stuff. My husband is allergic to wheat and I got a recipe for a flour mix off the internet that generally works quite well. His is not a full-blown gluten problem or celiac disease, so this is relatively easy. I don't know enough about the others to comment, so I won't.
I always ask if people really hate anything or have allergies or special needs when I invite them and then do my best to accomodate them. I suppose it is easier for me, since my kids and my husband were all allergic to different things and sometimes I felt a bit crazed trying to come up with meals everyone could eat. But we all survived, even thrived. Fortunately no one is allergic to tea, although many need to watch their caffeine intake.