They should emulate California. Go with a jungle primary and rid of those pesky Republicans in the general election.
In California the open primary actually improves the political power of Republicans in majority Democrat districts.
Because if two Democrats face each other in November (which is common) then the Republican voters come into play and they can elect the more conservative Democrat.
In the customary system the Republicans would vote for the GOP candidate who would then lose the election in a majority Democrat district and that allows the seat to swing further to the left.