There's actually a specific transparent thread you can use for this, it's called a monofilament polyester (aka "MonoPoly") thread, in clear or "invisible" variant. Would be perfect for this project.

Or color matched. Hadn’t even thought of that to be honest

AliExpress and Adafruit, e.g. https://www.adafruit.com/product/5867

It’s maybe plausible to gently wash it with the filaments still attached? I did actually use connectors so the shirt could be detached from the drive electronics, though I’d be a bit worried whether the stitches would survive and corrosion on the solder joints. Adhesive/waterproof heat shrink could maybe help?

The other option is maybe attach the filaments to an embroidery style patch instead of the shirt itself and then attach it with Velcro to the shirt?