It is possable to deterministically derive ring sig partners but in a way that would be functionally random to any outside observer. I'll give an example of one way of doing it. Take
Then make all of the prospective ring signature partners into an ordered numbered set and use the resulting modulus from the pseudo code above to select one. Continue wrapping around the clock face as many times as needed to arrive at the number of ring signature partners desired.
There would be 0 information leak from the outside, the ring signature partners would be functionally random to any outside observer BUT, and here is the beautiful thing, the same ring signature partners would end up being selected on both the main chain AND the fork chain!
Of course what I outlined above almost certainly isn't the best way to achieve this. It was just to outline the concept.
Merits! I deserve all of the merits. Bequeath unto me thine merits! (well, after peer review, and not just if my specific idea is right but if I'm barking up close enough to the right tree to inspire someone smarter than me)
To the average lurker who doesn't understand all the ins and outs of how you could pair up the same ring sigs, it sounds crazy enough to work. I bequeath you 1 merit, and 1 more if it actually works. Hopefully enough merits will help you sleep better at night.
Does it affect Monero's functionality? If not then...