Let's see what we have at the moment:
1. BM accepts all races without discriminating against anyone. She accepted Pekoms into her team, and Pedro with team, using this connection, entered her territory and tried to steal the poneglyph. And this made BM very angry, because Roger did the same. But, despite such a crime, she did not kill them and tested their luck. They were unlucky and lost their lives, and even so, she made concessions and let Pedro down alive, forbidding him to ever appear on her lands.
2.Pedro himself violated this ban(after all, there were many people who wanted to help SHs) and again penetrated into Tottoland with the help of Pecoms. And again they aimed at the poneglyph, killing and wounding the defenders of the castle.
3. They achieved their goals - they freed Sanji and got a copy of the poneglyph and could have left, but they stayed, deciding to save G66 and kill BM, on her own territory, in front of all her children, and even destroyed her castle, in which small children lived. The castle itself could kill a lot of harmless citizens if it wasn't for Streusen , but this didn't really bother Luffy and co.
4. As a result, the uninvited guests were cornered, and Pedro, attacking Prospero and blowing himself up, saved the others. The only fault of Perepro is that he survived this explosion and got up after it. Carrot saw this scene, and blamed Prospero for his death, although it was the choice of Pedro himself.
That I will note that only Carrot accused Prospero of killing Pedro, deceiving the other minks.