The usual argument advanced in favor of closed primaries is that a person ought to have some commitment to the party of which they're voting to select the candidate. The usual argument advanced in favor of open primaries is that all voters have a stake in who the parties nominate, and one ought not be required to state an allegiance to either of them to be able to have a say. I don't have strong feelings either way.
The thing I'm wondering about is whether the argument in favor of open primaries could also reasonably used to support allowing resident aliens to vote in the general elections. The situations seem analogous to me, but I could be missing something.