For me, it's got nothing to do with policy. Cruz could be a liberal and he would still scare me.
The thing with Trump is that he isn't an ideologue. Well, he's an ideologue to Trumpism, but not to anything else. Trump isn't beholden to any particular ideology, so I think he would govern with an open mind (for the most part). I think he's still nuts, but "everything is negotiable" to Trump.
Ideologues don't work like that. When confronted with a problem, the only solutions on the table are the ones in line with their ideology. This isn't unique to the GOP by any means, and there are plenty of ideologues on the left, but Cruz's particular ideology is insane.
Cruz is an extreme religious nut and believes he's been anointed by God to rule.
Cruz is a Christian Dominionist. His father is one too. You can search Google for scary quotes from the elder Cruz. There are a ton of them. His son's campaign isn't stopping him from talking either: this is from this week. The leader) of Cruz's PAC is one as well. They would love to turn the US into an outright theocracy.
If someone believes they have been chosen by God, then they can literally do anything without hesitation. If Cruz thinks God commands him to do something, then who could ever talk him out of it? His cabinet? The Joint Chiefs? Who are they compared to God? God tells him to carpet bomb the middle east with nukes to usher in the end times? God outranks the Air Force general saying it's a terrible idea.
It's also Un-American. It harkens back to when kings thought they were given power directly from God and were invincible. John Locke challenged this, arguing that power came from the people and not high above. Locke was a massive influence on the Founding Fathers (checks and balances came from him too) and they specifically rejected an all-powerful leader. I don't think there's a limit to what Cruz could or would do once he's in the Oval Office.
TLDR: Cruz wants to be a Christian King. Who could stop him once he took the throne?