''The Corsairs are currently involved in a long standing, large scale war with the Outcasts over the domination of the Omicron Edge Worlds.''
according to the Wiki.
It has also something to do with old grudges since Corsairs left the sleeper ship Hispania early after it got sabotaged by Coalition spies.
Sairs fear OC because of Cardi, they are scared to be enslaved to the substance, and OC hates Sairs because they left them to rot in the sleeper ship.
The millions of deaths on both sides during the war didn't make them exactly more friendly to each other.