Okay, this is from a square dance/contra caller: I'd go crazy if I was stuck with a single set of terms, no matter what they were.  The rhyming potential for the calls is lost.

Anyway, I still think it is more than just a matter of terminology.

All we are doing is swapping words; everyone knows they are stand-ins and what they are stand-ins for.  In essence, we are just obscuring the original choreographic intent of gendered figures and dances, not calling gender neutral dances.  (Plus, anything written within the last 30 years is a copyrighted work and technically we require permission to make changes, perform it publicly, OR make derivative works.  Not that anyone really cares.)

Personally, I haven't enjoyed the "gender neutral" dance events I've been to--not because I think it's a bad idea or dislike dancing with men, but because the callers were taking historical dances with built-in and intentional gender differences and simply ignoring them.  Particularly in older ECD, it is one thing to intentionally dance the lady's role and another to ignore that there WAS a role.  It impoverishes the dance as a whole.

Some older dances happen to work well as gendered or ungendered dances, but to me a truly gender-neutral dance is constructed to intentionally be that way.  For example, the following:

Gender-Swapped
By Neal Schlein, 5/29/15
Duple gender-less contra
Music: Probably something highly phrased, like Irish
A1: 1's step into center and handy hand turn neighbor 2 times
A1: End with everyone facing down the hall, 4 in line, and go down the hall
A2: Face the center of the line, pass thru, leads u-Turn and swing, any type (end in same spot where started swing, 1's on outside, facing up the hall)
B1: Come up the hall
B1: Bend the line and circle full
B2: 1's gypsy full and slow cast down while the 2's gypsy or swing 1 and 1/2 to end in starting line; 1s come into the center.

It's not the best timing in the B2, but if I did that right....
The dance itself is gender-neutral: it doesn't need gender or gender-substitute terms for teaching any of the figures or the sequence in any formation.  The choreography was selected to force interaction of identical sorts with all participating genders and positions.

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Neal Schlein