How Dany's inability to recall Hazzea name and her reaction to Viserys’s death are shamelessly twisted for a narrative of her as a heartless monster, another "seed" to her descend into madness by others, and how it's incredibly hypocritical of them:
It's enough for people to obsessively hate Rhaegar Targaryen for being one of many to speculated about the prophecy of Azor Ahai Reborn and wholeheartedly proclaim that Rhaegar was mad (as bad as Aerys) and has abducted and used Lyanna as incubator because of his "obsession" with said prophecy.
Despite both ideas not being backed up by the source material; i) Rhaegar is remembered fondly, capable and worthy (x, x, x, x, x, x, x) and "would have been a fine[r] king". ii) Rhaegar's "abduction" of Lyanna was even in-verse known to be motivated by (romantic) love, not because he believed her to be a part of the prophecy. (x, x, x, x) iii) Rhaegar believed the prophecy has already been fulfilled in his son with Elia Martell (x, x,)
Besides this, Rhaegar even had valid reasons (at least more than Stannis Baratheon ever had) to believe he could indeed be Azor Ahai; he was born amidst salt and smoke, it was prophesied that Azor Ahai Reborn will come forth from Aerys II and Rhaella's line (and for the longest time he seemed to be their only child to reach adulthood) he was the trueborn, rightful Lord of Dragonstone, "the place of salt and smoke" and dragons.
What takes the cake however, is their unironically projection of a character's flaw onto another, one that is designed to serve as a foil* and their refusal to apply the same moral belief system to all characters; they do not condemn Stannis Baratheon for his obsession with him as Azor Ahai Reborn and will use Jon Snow's parentage as proof that he is indeed Azor Ahai, using and validating the very same thought process they accuse Rhaegar of and condemn him for.
(*Stannis is a foil to Daenerys, and thus indirectly to Rhaegar, since Dany is constantly compared to him)
So while Stannis Baratheon can want to burn his child nephew, actually burn his uncle-in-law, consider burning newborn babes (x, x, x), loyal men (x, x, x) and will apparently burn his own daughter all for the sake of 'his duty' (x, x, x, x,) they will still proclaimed him as TKwC, The Best Man to Rule, while condemn Rhaegar and Daenerys Targaryen, mostly for sins they did not commit, but Stannis did; burning people and commit(/consider) atrocities with the excuse of being "The Chosen One" and it all being for "The Greater Good".