The two primary rule is a good rule
Political parties are private organizations, and they have the right to freedom of association.
The Indiana legislature just passed a law that requires a person to vote in two primaries. While "patriot" groups are very unhappy about this legislation, it is a good law that encourages better public servants. It makes sense for political parties to want to have candidates who are actually part of the party, not people jumping in after not voting in party primaries in the past. Political parties are private organizations, and they have the right to freedom of association. It also serves as a stop to people jumping parties after one primary vote.
There's no real way to ensure we have people with relevant experience running for office, but having people with a voting history at least assures that they have been doing more than voting in general elections.
There are objections: What about younger people? I voted in my first primary when I was 22, but I could have voted in the 1991 city election primary when I was 17. In Indiana, you can vote in a primary election if you will turn 18 before the general election. (I would have voted in the Democratic primary back then.) And perhaps having very young people serve in office should be something we should think twice about. Someone who is 20 years old has decades ahead of him to be involved and run for office.
In any case, this is not a blanket ban on people running for office unless they have voted in two primaries. A number of candidates had to get permission to run for office in 2010, because they voted in the Democratic primary as part of Operation Chaos in 2008. (Republicans were inspired by Rush Limbaugh to vote for Hillary Clinton to keep the Democratic primary going longer.) A county party chairman can approve a candidate who voted in the other party's primary or has not voted in two primary elections for his chosen party.
As private organizations, political parties have a legitimate interest in ensuring people who represent the party in a general election are part of the party. This encourages potential candidates to have a history of involvement in the public square and learn more about both campaigns and policy. No one is prohibited from running for office by the two primary rule. They just have to wait another cycle after another primary vote. It can also benefit challengers by giving them more time to prepare and raise money for a campaign. This is a good requirement and should remain in place.