According to Malcolm, Fabian Cortez and the Black Panther struggled for years over leadership of New Wakanda, which I think may be part of Malcolm's motivation for his attempt at taking over.
And you know, I can see his point. I can see why Fabian would feel that he had a right to New Wakanda. And no, I don't mean entitled power-hungry 616 Fabian, I mean Good Guy Good Leader Marvel Zombies Fabian.
Of the 12 survivors, only two (Forge and Black Panther) were not Acolytes. Fabian was the leader of the Acolytes. Fabian was also the one who saved Black Panther, despite the protests of the very Acolytes who would later follow T'challa in New Wakanda. And then they all spent five years in space together before coming back to Earth, presumably still under Fabian's leadership.
And then suddenly...Black Panther is the boss? And this is "New Wakanda" despite having no Wakandans in it aside from Black Panther himself? I can see why Fabian would feel this is unfair. And, since this Fabian was a good leader who cared about others, he might also feel that this was not the best thing for his people. They're all Acolytes save for Forge, and all of them including Forge is a mutant, and Fabian has been taking good care of all of them for years. Black Panther, as a human monarch and Avenger, may well not be someone that Fabian trusts to understand their needs, even if he may not have anything against him personally.
Of course, none of this means that the Acolytes/New Wakandans should have been ruled by anyone they didn't want to be ruled by. And I can see why they would pick Black Panther. While Fabian seems to have been a good leader during the zombie crisis, his leadership was in capacity as a combat leader. While we never see the Acolytes engaged in any villainy, as they're too busy dealing with the zombie threat, the fact that they followed Magneto is evidence they were supervillains (there are certainly differences in the Marvel Zombies world from 616 but Magneto was still a villain, pretty sure) and that means they a group regularly in combat or planning for it. That's a totally different ball game from living in a settlement and trying to rebuild life. The concern is no longer fighting the X-Men, acquiring weapons, infiltrating anti-mutant bases, etc. The concern is now food, shelter, settling inter-group disputes, just daily living. Black Panther, as a ruler of a nation, probably has more experience with that than Fabian does, albeit on a much larger scale.
This is not to say Fabian was a bad leader; he was a good leader in a specific situation. Black Panther was the better one in a different situation. Different times, different needs.
Which, to me, is a lot more interesting and realistic than "this guy was a 100% good leader and this one was 100% bad and also a meanie-poo" like usually happens in fiction.