They're connected to the audio ground plane, which is where they should be connected.
Unbalanced audio technically does not have and should never be connected to chassis ground - it has an audio ground and an audio signal. In this manner, a "ground loop" is not really what you're having, as a ground loop would short the voltage differential and flow current through the loop instead. The fact that you see a voltage difference implies that the separation is doing what it's supposed to. Instead, the problem is with whatever you've plugged them into, which probably.is a balanced-audio-capable input jack on a mixer which, by connecting it there, shorts the audio ground to the chassis ground AT THE MIXER which is not where that should happen - a balanced input should never bond signal and chassis ground together.
Instead, if that's indeed true, your situation is precisely what a DI box was created for, use those, or fabricate a cable out of XLR mic cable that is wired as follows: Shield to the Sleeve on the TRS connector, disconnected at the synth end. Ring on the TRS to white to the Shield on the TS end. Tip on the TRS to red to Tip on the TS end. That cable should kill your noise issue. If some small hum still persists (this is hit or miss) you can try to disconnect the TRS Sleeve entirely and leave the cable shield floating. DO NOT connect the white, the S on the TS end, or the Ring on the TRS end to the shield or the Sleeve on the TRS end.
While far from what I'd call readable these days, this document is technically correct, as long as you parse it very carefully and precisely and do not get confused about balanced vs. unbalanced:
https://www.ranecommercial.com/legacy/note151.html