There are religious conservatives that want to use government to legislate morality for everyone, but yes the term christofacists is not an accurate description.

Religious progressives is more apt. They hold many of the same positions as leftist progressives, utopian views on being able to control vice through authoritarian policies. Ban gambling, drinking, wrong sex, unhealthy food, etc etc etc. Only difference is they use religious justifications instead.

Apart from abortion and gay marriage they are essentially leftists. They can't even agree on these issues however which is why you'll not see them be able to agree on much besides being against the other side. They'll fall to infighting amongst themselves should they ever need to make policy and not simply counter policy.