In Chapter 1054 we see the Red Hair Pirates are sailing around Wano’s waters. Shanks reminisces about the time he stole the Gomu Gomu no Mi from Who’s-Who and CP9, and the time he spent with Luffy in Foosha Village. Anyway he decides not to reunite with Luffy just yet. He reminds to the crew that Bartolomeo made a mess recently in one of their territories by burning his flag and replacing it with Luffy’s and he wants to handle that situation. So he decides to go after Bartolomeo.
If you remember, in the cover page of chapter 875 Bartolomeo burned down Shanks’ Jolly Roger to the citizens’ horror. Now it’s not without purpose that Shanks goes after Bartholomeo and tries to kill him.
Shanks can’t simply not care here as most people believe. Bartolomeo has not only insulted Shanks but all the Red Hair Pirates. Shanks has to act on it because a Jolly Roger is the very existence of a pirate crew. If a crew does not respect it, it simply means they have no honour as pirates. That is why Luffy did not let Chopper’s flag to be dropped during the Drum Island arc.
Second, Bartolomeo burned Shanks’ flag which means he declared war against Shanks (when Ussop burned the World Government flag they said it meant the Straw Hats had declared war against the World Government).
If Bartolomeo starts hurting those people like he did on the last island, Shanks won’t just laugh it off. He didn’t get to be a Yonkou by going easy on pirates who torture and extort the people in his territory. Shanks is a good guy but still he is a pirate. Don’t forget what happened to Eustass Kid in his encounter with the Red Hair Pirates.
*Theory by GodSogeking