Relative to BfA's plot, it is without a doubt that Anduin misses his father and feels vengeful. Anduin despite being the faction's leader he would not get pulled into war so easily because he found some powerful crystallized blood. He wouldn't assassinate Goblins but rather try for a peaceful negotiation which is his character. He would've never tried to Siege Lordaeron. Greymane must've eventually told him all of the details of how he sacrificed himself and most importantly why: Sylvanas. She had told Varian she'd cover his flank from the ridge along with the rest of the Horde which prompt him to thank her and her wishing him good luck. This point forward if he had lived, the faction war would be over and Sylvanas and Varian would be friends.
However that isn't the case. Seeing Vol'jin suffering from a lethal wound, Baine overwhelmed by Legion forces and Thrall incapacitated, Sylvanas had no choice but to call for immediate retreat causing Varian to do the same as well which led to you know what. Getting to the point one could say Sylvanas caused his death indirectly which could be a fact causing her to be his murderer while another could say Varian scarified himself to save the Alliance but this could be countered since Jaina could've mass teleported everyone away or that Anduin would take over and Jaina, Varian, Genn, Tess and some Alliance soldiers would've died.
Seeing the Broken Shore as the root of the faction war that occurs in BfA if Anduin ever got the chance would he kill Sylvanas to avenge his father? Ask her why did she leave at the Broken Shore which may be the main cause led to Varian's death? What do you think?