Rough Roman Memes

Like I said,

Nowadays the problem is much reduced, and historians are generally more open to acknowledging the GSM identity or possible identity of historical figures.

As for Elagabalus specifically, Dio is one of the more reliable ancient historians, and does not assert that most of Elagabalus's behavior was private. Quite the contrary. Only a few accusations - such as the lurid and questionable claims about private religious ceremonies - are claimed to have been performed in secret. Most of the accused actions, such as the demand to be called a lady and not a lord to one of their male favorites, were purportedly done in public, which would make contradicting Dio's account much easier for any readers - especially as Dio was writing for an elite audience which would have likely had connections amongst Senators and Equestrians who would have had opportunity to see or at least rumormonger in Elagabalus's circle whilst alive.