According to TRA logic you'd both be agender as opposed to nonbinary. Because you specified that you and your partner do not have gender identities. Nonbinary refers to someone who has a gender identity that falls outside of the 'boundaries' of male and female, whether that be a mix of the two or an in between along a 'spectrum'. Agender on the other hand refers to the absence of a gender identity. Which, since you are both 'non men' agenders in a relationship, would make both of you pansexual. It is now a 'queer' relationship.

I wish I didn't know all of this. But I honestly think it's important to know how they think because then it's much easier to poke holes in their arguments.

For example: By their logic everyone except the most gender conforming individuals would also be agender. They say part of 'cis privilege' is never thinking about your gender. That if you think about your gender and question it, you are not cis. But then they go and make an identity for those who don't care about their gender. The aforementioned logic about 'cis privilege' has been thrown out the window. Because now every 'cis' person is agender due to the absence of a gender identity. Which is an oxymoron by their own definitions.