Oxalates are found in many foods, including spinach and beet greens. Here is a detailed article about what they are, what they do, and why some people might need to limit them.
I love Swiss Chard but shops don't carry it. Apparently it doesn't store well or long enough.
Swiss chard stems are not as tough and stringy as celery and I never throw them away. I usually cut them into short lengths and start cooking them a bit before the leaves.