At some point, taking a purely change-the-culture-first strategy stops being admirable and starts being naive and impractical. Most secular elites, whose whole worldview is based around the idea of individual autonomy, won't change their minds about abortion and same-sex marriage. By contrast, getting religious people and ordinary Americans to vote on issues they already support is not only more productive but also a lot easier.
Many cynics have claimed that the GOP could never actually enact "theocon" legislation and judicial decisions because they'd lose their juciest carrot for their stubbornest donkey. Such men might cite "changing hearts and minds" rhetoric as yet another delaying tactic, which is possible. However, I think cultural change advocates beat the culture drums for other reasons. I'll focus on pro-lifers:
First, they have some diffidence about their prospects of electoral success. Perhaps some think the electorate really is more on the side of the secular elites than ambivalent poll results suggest.
Second, cultural change is a vague concept, seeming to be above the rough-and-tumble world of lobbying, compromised politics, and specific policy recommendations. Culture means different things to different people, potentially fragmenting the pro-lifers' focus. Economic or social justice issues, crisis pregnancy work, and eroding libertine influence, though certainly worthwhile activities in themselves, lack the kind of unified effort that one specific law proposal can generate. At the same time, such efforts often make one think one is changing the culture more than one really is.
This is because cultural change will have few indications that it has in fact occurred until laws are actually passed. Granted, abortion rate decreases and sympathetic poll results are events to be cheered, but they seem too contingent a basis to announce that lasting cultural change has indeed taken place. Roe v. Wade signaled such a change for the worse. What else other than new law will signal a sure change for the better?