So at our dances (which always welcome a lot of beginners, maybe 40 percent or more), we have the tags at the front entry table and as people come in and pay, they are asked to choose a tag.

Our volunteers help ensure that roughly equal numbers of each are chosen, and once we start the beginner intro session we just switch a few folks if needed to get the numbers perfectly even

If two people come together, we suggest they each take opposite tags as it will ensure they get a chance to dance together

We are just very matter of fact about the fact that it doesn't matter which one you choose, and it seems to work very well for us.

I am also working on adapting any figure that traditionally relied on a gendered height difference, to make it work in a non-gendered setting.
(so for example, I might still teach a Cali twirl if it's the partners doing it because they can decide who steps under, but if its neighbours switching places I would use some other sort of tug-and/or-twirl-past-each-other technique, that doesn't involve an under-over dynamic...)

Kat k in Halifax NS