I think the back yard in all of these initialism is not limited to the person’s private back yard property.

NIMBY seeks to prevent the development of nearby properties to preserve some sort of “neighborhood character,” so the “back yard” is actually the whole neighborhood (and I think part of the negative connotation of that phrase is that they are treating shared spaces like their own personal yard). Then, YIMBY seeks to allow their neighborhoods to be developed.

If we’re going to extend it to “YIYBY” and “NIYBY,” we should apply the same logic, right?

Rather, I think YIYBY mostly doesn’t make sense because YIMBY people are trying to convince people that they should allow development in their neighborhood. Zoning rules… I mean, they have difference policies for changing them, but YIMBY activists aren’t usually manually and unilaterally changing them for other people.

Ultimately the decision making process is probably (depending on local regulation of course) “yes or no in our back yards,” when you get down to the details.

YIYBY is the concept of wanting it nearby to your residence but not having to suffer any of the direct consequences - imo it's a good thing to acknowledge but generally indistinguishable from NIMBYism. You want the benefits but aren't willing to pay the costs.