Kind of doubt the religious right is near as influential as they, and folks who worry about them, think they are. Pat Robertson, Jerry Falwell, et al., are really nonentities these days.
Even a secular society can benefit from a strict view of the constitution. The right to bear arms is a constitutional issue, where the ability to get an abortion if you want one is not. This is an issue left up to the States to decide - just as several States had already removed abortion prohibitions before the Roe v Wade decision. Social progress will go on absent court mandates. But, an Alito on the court may just stop nonsense like the Connecticut decision which allowed the municipality to take private property - not for public use - but on behalf of a private business entity.

I really think there is not much to worry about if Alito gets confirmed, just wish I could explain it better.