As a data point, when I switch back and forth, my alternate set is right up on the wall 8ft away in the rack. I've not ever had an issue with swapping, or the "other" set's TPMS interfering with the currently installed set.
I also have 3 TPMS equipped vehicles all in the same garage space, and they don't seem to jack with each other. (All FCA vehicles too).
But, going the other way ONE time I had a vehicle beside me in my truck as I was driving down the road set off my front passenger TPMS sensor. If I got either ahead or behind of them, it would return to normal, but if I was beside of them, my 60psi tire was only reading 30ish psi (I forget the exact number) But it was repeatable. Strange stuff.