How would automatic voter registration work with states using closed primaries?

[America Needs a 13-6 Progressive SCOTUS]

Do people automatically registered just end up ineligible for voting in primaries in those states unless they manually change it? Or is something else done? I might have a few follow up questions depending on the answer.

[Sestak]

In Oregon, yes, you're listed as unaffiliated and can't vote in any primaries. The same is true of Nevada (listed as nonpartisan), and I think Maryland too (though harder to find clear info on this). I can't imagine it working any other way, though.

[Tender Branson]

It's not impossible, because it is apples and oranges ...

One thing is to register people automatically, like virtually all European countries do.

Then, you can give people the possibility to register for a certain primary, for example by donating a symbolic 1€ to the party you want to vote for and sign up for that primary.

Or in the case of the US, where people are automatically registered to vote in some states via driving licenses, you could introduce an online/paper-form option to register by party as well.