I would extend this past historians.

A great example of the issue your looking at, and one you can see very easily, is the debate over Saladin's ethnicity (Was he Kurdish, Arabic, Turkish, Persian even?). I'm not super versed in the sourcing on it so I won't comment on it specifically, but you can see this conflict play out on his Wikipedia article's talk page very frequently. People can get pretty damn passionate about the question of Saladin's ethnic identity in the Middle East and it's driven by ongoing ethnic tensions, his culture hero reputation, and just the right amount of ambiguity.

The Aztecs developed an entire legendary origin for their civilization based on the Toltecs and the city of Tulla. They were actually practicing history and archeology when the Spanish arrived in Meso-America and Tenochititlan had a museum dedicated to who the Aztecs viewed as their cultural predecessors. This has caused quite a few eyebrows to raise in more modern times as archeologists have started wondering why the Aztecs found Tulla so important. In comparison to other cities in the region and time Tulla can seem kind of unimpressive in terms of scale and the city seems to have been smaller than many of its neighbors. While debate is ongoing there, lots of questions have been raised about why the Aztecs remembered the 'Toltecs' and their great city of 'Tulla' the way they did.

Absolutely, when people look back at the past there is a lot of projection involved and this has been an aspect of history since history began.

Historians are generally aware of this today (technically its been debated since ancient Greece but TLDR); it's called Presentism if we want to be technical, the injection of modern ideas onto past events. You'll more often see it simply called 'anachronism' and it's been a big taboo in professional history since its birth in the 19th Century and the Van Ranke school of thought. Though there are some historians like David Armitage who have argued that sometimes Presentism can be a useful tool, but he's definitely in a minority framing things that way. Still though, there is ongoing debate in the field about 'anachronism' and how it should be approached, avoided, managed, and even what is or isn't an anachronism (something out of place or time, like a fiddle in Imperial Rome or a modern conception of gender applied to a Roman emperor).

A good and early example of presentism in history is The History of the Decline and Fall of the Roman Empire by Edward Gibbon, which projects Gibbon's views of the Church into the past extensively. The entire concept of the 'Dark Ages' has been called out by many Historians as an anachronism, invented during conflicting forces of the Enlightenment and the Protestant Reformation to both explain the past and glorify the present. You might be aware of extensive political debates about Nazi Germany and gun policy, this is a very modern example of this in present day discourse.

The Nazis would never have conceptualized gun policy in the way a 21st century American politician does, but for the politician this anachronism can be a powerful rhetorical tool and for people it is an intermingling of cultural identity and the past that gives structure for their present. These narratives can be very powerful as a result, even when they're wildly inaccurate.

Historians have become very aware of this and within the profession it is treated as a bad practice. It can still happen though. Jared Diamond (technically an anthropologist) was accused of projecting modern ideas into the past by some critics when he published Guns, Germs, and Steel and Collapse. It's especially common in popular histories that cater to broad laymen audiences. Dedicated academics can do it to. A common criticism of literature professor Edward Said's Orientalism is that it painted oriental studies with too broad a brush and projected present debate on colonialism into the past. Even professional historians can do it though. It's a big problem in the History of Science as scholars try to tackle in our modern, data driven, age a past where scholars could be far more abstract.

If you want to know more about theory and practice of history, there's an excellent book from Arthur Marwick, The New Nature of History: Knowledge, Evidence, Language. There's also a favorite of mine Beyond the Battlefield: Race, Memory, and the American Civil War by David Blight. Blight's book can be dry at times, but its a great practical look at how shifting attitudes and memories of the past influence the present, how people structure the past to give the present meaning, and how historians do the best they can to walk a fine line between representing the past accurately while trying to make it relevant and useful in modern life.

While historians have broadly rejected many of the postmodern criticisms of our profession, we do owe a tiny thanks to them, primarily in how postmodernists called attention to an important reality: how people remember the past is ever changing and that memory can have an influence on the present.

This was as true 500 years ago as it is now.

So to your question:

So my question is, how much of historical judgement's about someone's identity in history relies more or less only on the identity of the historian?

I would say that professional historians are generally discouraged from and hesitant to make judgements about a person. HP Hartley is famously quoted as saying "the past is like a foreign country, they do things differently there."

I'm unfamiliar with Elagabalus (not huge of Roman history myself, only know the general overview), but I think historians are very torn over the modern issue of LGBTQ and how exactly it applies to people who lived hundreds and thousands of years ago. Homosexuality, bisexuality, intersex behaviors. None of these things are new. We have history for them going back thousands of years. But what they mean to us today, in the present, is often very very different from what they meant to people in the past.

Ideally, a historian tries to be neutral and tries to frame the past in its own context. But especially in the wake of postmodernism, we've become more aware that this is an ideal and even trying to limit bias doesn't eliminate it.

A historian looking at Elagabalus might talk about him in the context of modernity, especially in looking at LGBTQ history and what the past can tell us. I and many others however I think are very cautious in these matters, both because we don't want to offend people but we also don't want to twist the past into saying something it doesn't.

Perhaps someone with more specific knowledge of him and Rome will come along and give specific info about the scholarship on Elagabalus. I'm a historiographer so I'm much more comfortable limiting myself to the methods of history and how they apply to the issue you've run into.