Ruthless dictators can do much worse and still get by with a majority of the population being behind them in many cases. Fear and power is an important motivator for obedience. For the purposes of leading an organization under direct command of the WG, this alone is sufficient. He does not have to idealogically agree with all his subordinates. His superior accomplishments alone would be sufficient to shut up those who dont approve of his promotion.
At the end of the day they are all puppets and so you have to think about it accordingly. Looking at it from the WG point of view, people like Sengoku and Garp leaving their post at this critical time sort of makes it obvious that at some level they do not entirely approve of the WG's actions. To let a guy like Aokiji with a similar philosophy take the lead role is not necessarily a good idea. A person like him could idealogically influence the entire marine organziation to quite possibly turn against the WG in the future. Akainu on the other hand would be enough of a leader to lead the marines against pirates and criminals, but if he were to go against the WG and refuse their orders at any point, he probably wouldn't have any support. For them, it makes more sense to appoint Akainu because he poses no long term threat to them and can be quite easily replaced if need be.
There is no question that Aokiji would definitely make a better leader if the marines were an independent organization that upheld justice and were entirely driven by noble intentions. But they aren't so its a bad idea to have someone who can easily exploit confusion in the marine ranks that will result from being asked to do inethical things.