The author of this LA Times article seems to think there's a problem with the California Republican Party's only wanting Republicans to choose who will represent the party in the general election.
No one's being denied the "right" to vote in the Republican primary--register as a Republican, and you can vote for any Republican on the ballot. So what if the Democrats allow unaffiliated voters to vote in their primary? Why would you want someone from outside of your party choosing your party's candidate? I see too much opportunity for trouble there, and entirely support closed primaries.