I do not want to replace gent and lady as terms, based on my own experience.
Some context: I've been dancing for between 29 and 37 years, depending on how you count--my parents met at a square dance and I grew up dancing. I started calling about 18 years ago, and dance/call ECD, Scottish, squares, contra, ballroom, and folk styles at varying levels of proficiency. Seeing a man dancing the lady's role, or a woman dancing the gent's role, has never, ever phased me. It's fun to swap, requires technical skill, speaks well of a dancer who can do it well stylistically, and sometimes is necessary to fill out a set. It is also an important skill for any caller, and one callers need to know how to handle when it happens in special situations; the callers I grew up with talked about when they first encountered gay or one-gender crowds in the 60s and how they struggled to adjust on the fly.
That said, I first encountered "gender-free" dancing at a Heather and Rose (?) ECD dance outside of Eugene, Oregon about 15 years ago. I didn't know what I was walking into, and thought it was a normal ECD event until they lined up and started teaching.
They used several dances I was familiar with; I had been teaching some older ECD dances for a graduate folklore class and recently returned from Berea's Christmas Country Dance School. Aside from momentary confusion, adapting to the unfamiliar terminology and random line-up was not a problem for me.
What I couldn't adapt to was how being made "gender free" changed the character of the dances I knew. They became less elegant, less interesting, and were lessened overall. Switching between an A and a B position meant nothing aside from (possibly) a slightly different floor pattern. Proper and improper had no relevance. There was no stylistic mastery needed to switch dance sides because any clue as to historically demanded or intended stylistic differences had been stripped out--there weren't even ROLES anymore, merely positions; there was nothing to hold onto even as a guideline for playacting. The dances completely lost their flavor and character. They became like Caffeine Free Diet Crystal Coke. (I mean, honestly...WHY WAS THAT EVER MADE? Just drink water!)
Other folks may certainly disagree with me, and I have followed and agree with the many counterpoints, but I personally believe that the terms "gentlemen" and "ladies" (and their derivatives) positively influence how people behave and relate, and definitely how a dance is done. I don't worry about that at special or family events, of course; I just want everyone to get up and have a good time. But encouraging folks to learn both roles to become better dancers is only meaningful if there is a meaningful difference between the roles.
I am a happily married man and prefer to dance with women as partners and corners. I don't mind dancing with men, but that's not what I go to dances for; if I wanted to get close to a bunch of sweaty guys, I'd play football. If we're honest, we can admit that the vast majority of our general dancers (both new and old) are probably similar. So why not let the dance reflect that? That's more likely to win friends than taking a wonderful dance with character and making it into "gender free diet crystal contra."
Just my 2 cents.