Nonbinary

yes, this is a very important point - many non-binary people experience dysphoria, and even worse they don't even have the same options to treat or deal with that dysphoria that a binary trans person might have like medically transitioning. If you're a transfem enby who experiences dysphoria from female breasts but also feel dysphoria from a male body ... your options are much more limited than a binary trans woman who feels entirely at home in a female body.

Furthermore, there isn't the same social space or recognition of genders besides men and women, making it harder for enbies to be recognized as anything but their assigned gender even when they engage in gender queer expression. This is incredibly alienating in its own right, an outright denial of that person's gender.

While a binary trans person might just feel anyone who is not transitioning is categorically in a better situation (i.e. not oppressed and so on), I think it's obvious that this isn't the case for a lot of enbies, even if it's true that the ways oppression might work are different (e.g. by conforming and not transitioning, some enbies might be de facto safer), but like you said - this is true of binary trans people (both who remain closeted and don't transition, and those who transition and are able to pass as cis on the other side of their transition - both remain shielded by cis-passing privilege).

EDIT: I sorta failed to answer your question:

Everyone could technically deny their transness and go with cis normativism. ... I don’t get why that should be different for binary and non binary trans people.

I think in the mindset of the people who are having these strong feelings is that transitioning involves huge risk and cost that people who don't transition aren't experiencing.

You are right that trans people who stay in the closet are just like enbies who are cis-conforming in that both of them avoid the risks involved in transition. I don't think this view is necessarily wrong (i.e. transition does have risks that not transitioning doesn't have, and transitioning does lead to losing cis-conformity privilege).

The way this view gets applied is often wrong, I think because there is a psychology of feeling your risk and suffering as someone who transitioned makes you categorically different, and that the political categories are based on oppression reinforces this sense of difference.

It's also usually emotionally charged, it's not like we're talking about the distinction being used in a neutral fashion - OP was told they were told they weren't "really trans" as if the umbrella term only designates people who medically transition, and their entire experience as a trans person was called into question because they didn't conform to a particular way of being trans (of being binary, medically transitioning, etc.).

So you're right, they're not different, both binary and non-binary trans people can experience cis-conforming privileges by remaining closeted. The differences don't really seem to be about binary vs non-binary, since both can involve cis-conformity, both can involve dysphoria, and both can involve medical transition.

Maybe the hostile trans woman from OP's interaction was operating with generalizations like non-binary people not commonly experiencing dysphoria or not commonly medically transitioning, but these just are just generalizations, and they don't hold true for OP and plenty of other enbies.