I've never seen this style of fastener for a faucet stem.
It doesn't seem to be screwed into the threads.
I need to replace the faucet and I have no clue how to disassemble it.
How do I remove this?
EDIT: Extra photos
The inside side is much like the front. You can see on the far faucet stem what the side facing the center looks like.
A closer look at the threads. The "fork" piece seems to be clipped onto a ring that is screwed onto the threads.
Best Answer
Difficult to be sure, as I've never met one in person before, but judging from what I can see in your picture I suspect there is a part on the threads, but there also appears to be a pin (on, I think, that part) through the side of the "fork" part, and I suspect you can pry the left (open) side of the fork to pop the hole in the fork off the pin, while pulling or prying to the right. Presumably there's another pin on the other side to get the "fork" off of before it will come free.
You might try unscrewing it a turn or two (I'm unclear if you have made this attempt yet) to make it easier to pop the "fork" off. My guess is that this arrangement is intended to allow the part on the threads to pass through the hole so that rather than having to turn the nut on many turns in an awkward location, the nut part can be pre-located close to snug, the faucet inserted, and the fork clipped on and tightened only a turn or two to hold onto the sink/countertop/tub.