I studied Roman history in college. So the urge to write a giant wall of text about this is pretty strong. But I recognize many people find this shit boring so I'll keep it short.
Based off of what I have read in Cassius Dio, I don't think calling Elgabalus a tranny is an unfair assessment. He would definitely fall into the category of an HSTS though. I've provided a link to a free translation of the relevant chapter in Dio below. As well as another website summarizing the 3 extent primary sources that cover Elgabalus.
Now the original Latin or Greek might describe him differently. I can't speak to that. I don't know enough Latin anymore to read a whole page of text and I never studied Greek. A lot of free translations are old though. The one I linked was published in 1927. So I doubt the translator had any particular interest in presenting Elgabalus as a tranny icon. I've seen people mention that the authors of the primary sources could be biased in their description of Elgabalus. Well that's probably true at least to some extent. But these texts are all we have. So that's that.
They can call him a tranny if they want to I guess. Maybe in 20 years we'll go back to calling him doubtlessly what Roman historians of the past thought of him. A deranged incompetent faggot who drowned to death after being thrown in the Tiber.