Protecting the institution of man-woman traditional marriage is not mandating Creationism in science classes, for goodness sake.
That, as you put it, time-wasting straw man gay marriage argument happens to be a proven vote-getter, an overwhelmingly popular political position which cuts across virtually all political demographics in Blue and Red states alike. It's about as sure a winning issue as exists in politics. The suggestion that it's a political loser for Republicans which emanates from the fringe of puritanical Christian zealots out to control the lives of others is risible.
The gay marriage issue is about as bad an example as one could use to attempt to make the point you intended to make.
factoid:
In 2000, 61.4% of California voters passed Proposition 22, the California Defense of Marriage Act, barring recognition of same-sex marriages.