Sort of open, sort of not. If you're a registered Dem or Rep, you can't vote in the other party's primary. If you're independent, you can vote in either, but not both. IOW, if you want to vote in the GOP primary for Senator, you can't vote in the Dem primary for Governor.
As for taking it up with the Republican party, it was taken up with them a couple months ago, and it was voted down. It's not called "The Stupid Party" for nothing.
You do know there are a lot of registered independents in AZ.
And why would a registered independent vote in a Dem primary if there is only one Dem candidate running for any given biggy state office?