This is where I differ. Its the "purists" in both parties are the ones who have been most likely to get out and vote. Always has been.
Historically its been the "independents" - middle class low info voters - who unless given a clear reason to vote tend stay home.
For example, ever since the republican party ceased being the party of 'ideological' Reagan and became the 'pragmatic' party of Bush, the Reagan Democrats have migrated back to their sofas, or worse, back to the democrat party.
Its the GOP's job to win them back. But they are unable because they really do not believe - never did believe - in the conservatism as Reagan expoused.
Not ‘differing’, you are astutely pointing out another dynamic, one that sometimes works for, and sometimes works against either side:
the purists who select the nominee are the ones who will man the phone banks, contribute early and do the hard work, so candidates run to the far left and right in the primaries. And then they run to the center for the general election, or at least change their message points to appeal to the ‘center’.