The Twenty-Sixth Amendment provides, “The right of citizens of the United States, who are 18 years of age or older, to vote, shall not be denied or abridged by the United States or any state on account of age.” ... Like many other amendments, it was enacted as a direct repudiation of a U.S. Supreme Court ruling.
Only registered democrats would be able to vote in an open primary election to choose a candidate for the senate, although it should be noted that there are exceptions.