It's a catch 22. I like buying stuff from the states but it costs an arm and a leg cuz our dollar sucks. But because our dollar sucks American productions come here and I make more money.

Toronto! Hey, you're the ones taking all our SAG/AFTRA work away from us Californians.
Send it back immediately with an apology.

Nothing to see here, move along.

As an actor myself with a few credits on imdb and also friends with several actors there are things I want to point out.
Day players or one liners on a movie or show might not get a screen credit. For example, the truck driver who found Iron Skye and the woman who pulled over to see the Truck Driver and Skye/Kathleen are considered day players who had less then 5 lines. They probably went in the credits either.
Neither were the CIA, FBI, etc. that we're in the cipher scenes and speaking or the waiter at Graysmith/Melanie's first date received a credit.
Some of them are just tax credit roles. I live in Toronto and when they film movies here producers want to hire X amount of actors for just one liners even give it to an extra for tax purposes. Anyone could have played that part so they are meaningless credits.
Now aside from all this one thing I read was the Directors Cut does list a lot of the uncredited actors from the theatrical version. My guess is because the movie was already over 2 hours and the studio wants it as short as possible So they can play it more in theaters a lot of people werent credited.

Credits inclusion and placement are negotiated case-by-case between the filmmakers and the talent, usually through the talent's agent.
As BillK-5 notes, reasons vary. We can't know why Skye chose to go uncredited unless she chooses to go public with her reasons.

Nothing to see here, move along.

Did not even recognize her but as low as the radio music was in the beginning of the shooting scene recognized Donovan's "Hurdy Gurdy Man" instantly. The song was not Fincher's first choice FYI but was a perfect selection.

Usually one of two reasons:

1. They're doing the role for fun, as a favor to someone (friend of the director, etc.) and/or were willing to work for scale, or as a cameo.
2. They don't want their name to be used in publicizing the film (not because it's bad, but because they want their involvement to be a surprise or for you to concentrate on the character they played, not that it was them.)

Robert de Niro in American Hustle is another great example.

I've always wondered, in general, what dictates that someone is "uncredited". I use to think it was due to lack of spoken dialogues, but there are plenty of instances in films, like Iona Skye's role, where the actor/actress does have lines yet remains uncredited.

Ahh, interesting. Thanks.

I think they just had her in there as a clever connection to her dad Donovan, who sings the closing credits song, "Hurdygurdy Man."