Not all independents are the same. Some independents vote for the most conservative person republican or democrat. Many independents held their nose and voted for John McCain.
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That being the case, they should ID themselves as Conservatives, imho, and remove all doubts.
When I go to vote in the primary, they ask me which ballot Republican or Democrat? Conservative is not one of the options.
I'm not sure that's an option. The Conservative Party (no idea of whether it's affiliated nationally or what) once did get enough votes to be an "official" party in MA (I think in 1996, when it ran Gallagher the year Bill Weld challenged Kerry) -- but they've never run a candidate for anything since.
In any case, to register as a Conservative would mean in practical terms that you couldn't vote in a primary -- God knows there are few enough meaningful Republican primaries in MA. An independent ("Unenrolled" here, since a third party took the name Independent) can vote in whichever primary looks more important to him.