Why not vote in the Democratic Primary if you're Republican?

Actually, the term “political party” refers to very different things in the US and most of the rest of the world. In most countries, at least in Europe if not worldwide, parties are associations with statutes, local charters, a fixed and standing hierarchy of elected officials and councils, and formal membership.
The German system can be summed up like this:

If you join a party (which is done by filing a written request), you become a member in a local charter of that party, of which practically every town has one. The various charters are allowed to elect delegates to represent their charter on party congresses on regional levels. The regional levels similarly send delegates to the party congresses on the state level, and IIRC it’s also the regional levels that elect delegates to the Federal Party Congresses that are usually held once a year. Those federal congresses elect the party’s federal cahirperson, a board, and similar institutions that exist permanently. Fixing the candidates for elections is usually done by those institutions as well, without any involvement of the members themselves (although some parties are considering the introduction of internal elections to determine their candidates, but this hasn’t been done yet). The party maintains some sort of bureaucracy, and its source of funding are mainly membership dues, donations, and subsidies allocated to them by the state (yes, tax monies) based on the vtes they got in the last elections. Party funding is a constant source of scandals in German politics.

Generally, party membership is not too common. The largest political party, the SPD (of which the current chancellor is chairman) has about 650,000 members in a nation with a population of about 82 million. The other parties traditionally have much less.

In the last place I lived, the city council elections included accusations that significant numbers of Republicans were voting in the primary to try to elect the candidate they believed would be easiest to beat.

Um, it was clear in my last post that the Republicans were voting in the Democratic primary, right?

Should preview more often.

That’s a decent idea as far as it goes.

My parents were of the opinion at the time that the Dem candidate was going to win in MO no matter what, so they voted for the one they could stand the most in the primary.