Dany seemed inclined not to believe the news at first. She questioned the sources: Jon's best friend and brother. But she did let go of Jon in seeming disgust when she initially learned they were related. However, for Dany, the pain of Jon's reveal goes deeper than their accidental incest. She's only ever wanted to rule the Iron Throne, largely because it was rightfully hers, and now Jon has a stronger right to rule than her (thanks to patriarchal BS existing even in fantasy worlds). "If it were true, it would make you the last male heir of house Targaryen," Dany said to Jon. "You’d have a claim to the Iron Throne." But their conversation stopped short when the alarm horn was blared. Jon and Dany had to set aside this strife and prepare to fight.