I ended up contacting Sequential support mostly because I was curious about the behavior. Not really any real problem in the big picture, but why only bank changes? Why not 10s and 1s?
For starters, according to the support person I was in contact with, there is no built-in way to prevent the patch changes from being sent (and received) in this situation where the Prophet is sending MIDI directly to the Trigon. The explanation being that the expected use case is to have two of the same units polychained together. In that situation, it makes sense to have the receiver follow along exactly.
The support person had me set up the simplest routing. One midi cable from the P6 to the Trigon. Being a software dev, I should have done that on my own from the start ... basic debugging skills apply to the real world as well. But I often forget. Nonetheless, after doing that, then it became clear that all patch changes (bank, 10s, 1s) affect the receiving unit.
He suggested, as a possible solution, an inline MIDI filter and provided a possible vendor. I then remembered that I had set up filtering in my current setup which led to the puzzling situation. And then I said to myself, "Sheesh, Mark, you gotta learn to think for yourself if ya wanna survive in this world!" And then I responded to myself ... but ... I digress uselessly.
My current setup to connect my various hardware synths is an mioXM from iConnectivity. It's pretty cool and allows me to run a USB cable from each synth to that unit. And then I can set the routing however I want (synthA can send midi to B and C, and C can send midi to D, the DAW can send midi to one or more synths from multiple tracks, etc.)
The other bit of functionality in the mioXM, however, is some filtering options. And I had (a long time ago) set it to filter program changes from the Prophet 6 on all midi channels. That is why the 10s and 1s on program changes did not reach the Trigon-6. I don't know 100% for sure, but I'm guessing the bank changes are in a different MIDI category (at least by mioXM standards). In order to prevent the bank changes (e.g., bank 3xx to 4xx), I had to filter out control changes. Once I filtered those as well in the mioXM, I could changes patches on the P6 and have no affect on the Trigon. Of course, that also filters out things like sustain messages, so that is not a useful option for me. But at least the mystery was solved. I don't think the mioXM has filtering at a lower granularity ... at least not that I have found. Probably need to apply some more software debugging methods.