The libertarian streak is pretty strong in Cruz. He is an evangelical and is at home standing up in churches, but he has not run a traditional Bible-waving social issues campaign. His big issue in this area is religious liberty, which is a different matter. The left is hell-bent on eradicating any lingering vestige of traditional Judeo-Christian sexual ethics in the public square and forcing all institutions and businesses to conform to a radical new orthodoxy. Cruz is fighting for the right to be left alone, which implies the right for religious conservatives to build a viable counterculture, including businesses, schools, hospitals, universities, charitable organizations, etc. that adhere to traditional norms.
I don't think most people on the left understand, or care about, this distinction. They think they have finally gained the upper hand, and they are determined to enforce total compliance. It might be possible to reach a settlement along live-and-let-live lines, but the radical intolerance of the left has to be defeated. That's the Cruz issue.
Neither Trump nor Kasich, btw, show the slightest glimmering of understanding of this difference as well.