Why does my patchwork mug keep cracking at the seams?

Your classmate is onto something, but it's only half the story. Shrinkage rates do matter, but the bigger killer with mixed bodies is that they move differently at different stages. Earthenware and stoneware don't just shrink at different amounts, they shrink at different times during drying and firing. The white stoneware does most of its shrinking later in the glaze fire as it tightens up, while the earthenware is basially done moving by then. That's exactly why your cracks opened wider in the glaze fire instead of showing up earlier. Plus if you fired to stoneware temps, the earthenware is getting pushed way past where it's happy, which makes it do weird things at the seams.

I fought the same war with mixed-body teabowls a couple years back. What saved me was mixing my own slip with a pinch of paper clay fibers in it. Regular slip scored-and-slipped joints kept opening on me too, but the paper fibers kind of stitch across the seam while it dries and give the two bodies somthing to flex around. I also started drying the whole thing under plastic way longer than felt neccessary, like a full week. Now I only pick clays that are within a couple points of each other on the shrinkage chart, and honestly the paper slip did more for me than careful body matching did.

Honestly, my fix was dumb and simple: I stopped pushing mixed-body pieces past cone 6. Fired my patch stuff at cone 04 glaze instead and the seams stayed put. The earthenware is happy there, the stoneware just looks a bit softer and more open, and the dark speckle glaze still covers fine. One of my mixed slab planters has survived two winters outside on the porch with no spalling, so it's not just shelf art. If you can live with a lower temp glaze palette, that alone might kill most of your seam trouble.

the cone 04 advice matches what worked for me. I make mixed slab planters with red clay and white mixed togather and they only survived once I dropped the glaze temp way down. One extra thing that helped: I roll a thin snake of the softer clay and press it along each seam before it dries, like a bead of caulk. It gives the joint a little cushion instead of two hard faces butting up against each other. My last batch got thru three firings with maybe one hairline total.

Update: tried the paper clay slip trick on a test tile pair, one white stoneware to red earthenware, and the seam actually held through drying. Went ahead and bisqued it. Before I glaze fire, one thing I'm unsure on from the cone 04 posts: do you still use your regular glazes at that temp or do you need low-fire ones? I only own cone 6 glazes right now.