I just found out that Speedball Screen Drawing Fluid and Screen Filler (for fabric printing) are both non-toxic. Which means that my whole printing set up is actually non-toxic. Honestly, I just grabbed the two smallest bottles of these products available without knowing about their toxicity because I didn't think I would be doing much beyond stencil prints.
But now I find myself quite encouraged. Although I do feel a bit silly for wearing rubber gloves as I worked last night.