States handle primary voting in many different ways. In Maryland, many conservatives stay in the Democratic party because there is almost never more than one entrant in the Republican primary. The above mentioned conservatives were the "Democrats for Ehrlich" that helped us get a Republican governor for the first time in decades. An Independent can still vote for school board members. If anyone doesn't like the way his state handles primaries, he can try to change things.
No, actually they cannot. Since the Supreme Court has "made new law" in this area, it cannot be overturned by "mere voters". A large majority of voters are in favor of the "open primary"---but the Dem and 'Pubbie power stucture aren't.