Someone actually considered a solution I approved of (and actually advocated for) Have the awards broken down by portrayal of a character, not the actor. This would follow the category of performance of a female character, male character, non-binary character.
As someone who always welcomes the idea of more awards, not fewer (at least in TV) I Tthink this would at least partially solve the debate. Non-binary performers wouldn't have to compromise if the awards were given for the character they played rather then the gender of the category and it wouldn't cause the inevitable backlash that getting rid of the gender distinction would. I'm a pragmatist: I think actors in Hollywood are for this as long as its theoretical. As soon as this starts being carried out in practice and, well let's be honest, males start getting shut out, there's going to be more outrage in Hollywood about this.
I don't deny the issue is difficult: as someone who admired Asia Kate Dillon's work on Billions I did think it was unfair that there wasn't a category for them to compete it. But I know this industry and I know everyone in Hollywood is liberal until they start losing out: then their radical conservatives. I think this solution I suggested is a compromise few could srgue with (which means everyone will ;)