With the latest chapter, we can see how an event over here brings about consequences elsewhere.
The fall of Doflamingo directly caused wars to end due to the shortage of illegal arms. Those who are happy with this event will hail Strawhat and Law as saviors while those unhappy pins the blame on them at the same time. Inadvertently Strawhat and Law simultaneously makes friends and enemies all over New World.
As a direct effect, Kaido (and quite possibly Drake) will come after them, but we already knew this upfront.
The revelation of Kid alliance going after Red Hair Shanks will also carry a significant effect. Shanks, to-date, is not known as an oppressor. Thus being a Yonko, I got the impression that he genuinely protected those under his territory. Should Kid alliance succeeded in bringing down Red Hair pirates, everyone under his territory will plunge into a state of chaos, with opportunist rogue pirates and/or other Yonko pirates taking over, beginning a new era of oppression. Thus those under Shanks will resent Kid alliance for putting them into this state.
When the news of Kid alliance campaigning against Shanks reached the Strawhats, then Luffy and the Strawhats will be in a huge dilemma. They have already earned the wrath of Kaido and Big Mom and Luffy may want to instantly drop everything and go after Kid alliance or help Shanks but in doing so will mean betraying and dumping Law to deal with Kaido on his own. And in the midst of this chaotic state, there's Blackbeard and the opportunity is present for him to take advantage of, whether it is to hunt DFs or take out oppositions.
Thus unlike Paradise where the political balance is pretty much independent from island to island, everything that Luffy does in New World will have a profound effect and making friends (or shippers) as well as enemies at the same time.