A caveat to start: I’m not going to make the case for fully open primaries. That is, I don’t think registered Republicans ought to be able to vote in the Democratic primary or vice-versa. And I even support the idea that if one wishes to switch parties one must do so some (reasonably short) time before the election.
But I do think it’s beneficial to the party to allow people with no party affiliation to vote in the primary, the reason being that we want (or at least ought to want) to draw those people into the party. And for the most part these unaffiliated people are not the heavily engaged political animals we are — they probably don’t pay much attention to the race until a couple of weeks or less before the primary, when the candidates begin campaigning and advertising in their state. So for instance here in Florida, where one must make any party change 29 days before the election, it’s already too late.
I understand the arguments about malicious strategic voting but frankly I doubt that’s a big effect, particularly if one doesn’t open the primary to registered Republicans. I think the potential to grow the party outweighs that risk.