Technically, this is debatable. Technically, the rules say that fear attacks are always mind-affecting—leaving room for fear effects that are not fear attacks, so would not necessarily be mind-affecting, and so in theory, there could be fear effects that someone with mind-affecting immunity is still subject to.
In practice, it is almost-certain that the authors were using attack and effect interchangeably, and that all fear effects are definitively mind-affecting, and so fear immunity is a subset of mind-affecting immunity—which means that mind-affecting immunity is fear immunity (and then some). I doubt you will find many, if any, DMs, who will buy this argument and allow someone with immunity to mind-affecting effects take Craven.
All that said, on balance, the inability to get mind-affecting immunity is a huge drawback to the Craven feat. To the point that, at higher levels when a rogue should be considering a source of mind blank, as important as the damage bonus from Craven is, sooner or later the immunity to mind-affecting is more important.
So that leads us to a question: is it a good thing that Craven eventually becomes a negative effect, and so high-level rogues avoid it? On the one hand, Craven is a large damage bonus for rogues and the like, far better than almost any other feat would be for your typical two-weapon fighting rogue. Even more so when you’re looking at a multiclassed character whose sneak attack isn’t as good as a single-classed rogue. If it didn’t have that drawback, every sneak attacking character ever would always take the feat. That’s bad—feats should be options, not mandatory. Something that’s too good becomes centralizing, since everyone takes it.
However, another thing to consider is, sneak attackers simply deal less damage, a lot less damage, than other martial characters. The benefits of two-handed weapons, charging, and so on are all far larger than sneak attack, even with Craven. So if rogues and the like are avoiding Craven because of its drawback, they are then even worse off than they would be. From this perspective, Craven-without-drawbacks might be considered better for balance—sure, every sneak attacker will always want to take it, but at least once they do they’ll be closer in damage. Consider: Power Attack can deal literally twice the damage that Craven does, and the attack penalty is far easier to deal with than Craven’s ban on mind-affecting immunity.
So while almost-no DM is ever going to buy the argument the attack vs. effect argument for allowing someone with mind-affecting immunity to take Craven, some DMs might consider allowing it as a houserule. It may be worth asking.