This just seems like a really alien view of US politics. It is just not the case that voters are only interested in having a representative who votes the right way on some set of issues. Voters want representatives who represent them. And this isn't entirely crazy - part of the reason we have representatives at all rather than just doing everything by direct democracy is that the voters aren't supposed to be qualified to come to the right decision on many issues and are instead supposed to appoint people whose judgment they trust and whose values they agree with to make those decisions for them. Hypocritical or otherwise insincere politicians break the system - they take the positions they take so as to signal to voters that they're the right sort of person, but aren't actually guided by these values in making decisions that the voters aren't micromanaging. Or, worse, they might actually be abusing voters' trust to win support for things that the voters really wouldn't support, absent trusted authority figures telling them it's consistent with their values. You can argue that the voters are too easily outraged by minor bits of wrongdoing, but this is a pretty serious wrong in itself and the hypocrisy is especially problematic given the importance of "family values" to the voters.
But you're right that "this isn't an Eich situation". Here it's actually smart to make this guy the poster boy for the anti- SSM movement and to emphasize how judge-y of other people's personal lives the "family values" stuff is.
