Imagine a person who says they are a furry. What makes them a furry? They don't wear a fursuit... They don't attend conventions... They don't watch cartoons or read manga or comics with furry characters... Really, more than any of those things what makes them a furry is that they say they are: that they identify as a furry.
No presence or lack of a particular behavior is going to make them not-a-furry. Other furries saying 'you aren't a real furry' can only possibly be talking shit.
They may not want to hang around our example, they may not see much in common, and that's OK. It may even be valid to say 'you aren't furry the way we are furry' or even 'we have very different ideas as to what makes someone a furry' and THAT may certainly be true. But it also isn't a choice as to what someone's interests are, or what classifications they understand as applying in what circumstances.
Telling them that they aren't a furry isn't OK. It's an act of social aggression to invalidate their identity.
Gender identity is much the same way, albeit bolstered and made more concrete, more urgent and necessary to respect by the fact that biology rather than merely psychology factors into it: many parts of the brain differentiate on the basis of particular things that happen at various stages of development that predispose them to certain behaviors that we teach as being either "masculine" or "feminine", and to both aspiration to, and attraction to, particular body types and invasive thought patterns which we also associate with masculinity or femininity. And these body types and invasive thought patterns are the product of exposure to hormones and how those hormones interact with the brains that aspire to them.
In this way, of interests predisposed to us by some aspect of life, being a man or a woman is much like being a furry: it is about self, not about society. Society merely provides the menu, and our gonads merely provide the push towards a particular selection on that menu when we fail or otherwise cannot order for ourselves, often an order we would rather repugnant to have upon our plates.
The point is, identities don't come from.other people. Their existence comes from society, their acceptance comes from whether we think we fit that social category. It is appropriate for others, at most, to say whether or not we are doing it well, not whether or not we qualify.