I am not the parent comment, but I would also refuse to give you a label. The very request is disagreeable, not whichever label it is that you use.
In all ways I am how I was born, and I have no desire to have that impact who or what I associate with or how I associate with it. I have to deal with these things when it is obvious to peoples eyes how or what I might be, I have no desire to add to it with intangibles. This feeling should hopefully be familiar to you: It should be the feeling you have when you are in the minority in any way considered important by those around you or those you care about, but especially so when it is not relevant to most of anything.
My relationship with non-gender-related aspects of myself follows this same pattern: Autistic or not, ADHD or not, I have no desire to be categorised as neurodivergent, neurotypical, neurospicy, or any such term. These are epithets all and the use of them when discussing specific others, even when benevolent, is almost always in a way that serves to other. And they are terms that will almost inevitably be used as deliberate insults.
Downthread, you mention that you call yourself queer but you would reject that label when applied to you by others. I cannot help but think that your feeling there is similar to a number of other people's feelings about the parts of their identity that they do not wish to label; I do not wish to label myself, so please do not label me.
There are others who may wish to identify with a group or a label because it is a part of their identity, and because that label comforts them or softens the edges of how society may treat them or whatever it might be. For most of those who are objecting to the cishet label, I suspect you may find that it has almost always only been used in their presence to discount them or their opinions. This is not the fault of the label, but its intent, for many. There is no trick of semantics that you can pull to strip the label's fundamental semiotic purpose, which will inevitably be used for scorn, as always.
What you are asking, in this case, is to put people on the treadmill.