I wouldn't mind having a deity specific skill based on which one you chose, though if they included this, they would also need to include the option to change your deity, and thus the skill you have access to. Over time people change from loving one type of class to another, and being stuck with a deity skill that increases magic damage for 30 seconds would be useless to a Warrior, as would a TP regeneration skill to a caster. Still, make it so you can only have one available at a time, and maybe you have to use Grand Company seals to change it, such as when you reset your skill points, (plus it would give us more use for Grand Company seals late game beyond buying Ventures).....
EDIT: That being said, I see no reason for racial skills. That would break the balance of the game, as everyone would determine that certain races are indisputably better for certain roles based on said skills, and should your skill be useless to your play style you would have to use a fantasia to completely recreate your character's identity just to get one you found more useful. Racial benefits were always one of the most annoying aspects of games like The Elder Scrolls, as they meant you either played with a race based on what was better for your style, or you played with one you liked the looks of and sacrificed a lot of your potential. As is, there are slight racial benefits, but they're ultimately minor. Unique abilities would not be minor by any means however.....