Santa Vaca is something John Wick posts about, often ideas on modifying the rules of D&D for more story than mechanics. Here's a suggestion I have, and how alignments relate to Crux, since its the most prominent in my mind. The Pathfinder end of Crux uses Alignments more inspired by Eberron or Arcanis to a degree- alignment isn't predictable, and religions aren't bound by only one alignment. Anyone or any faith could be of any alignment.
So most of the normal restrictions on alignment become based on personal choice, not some moral choice on a macro level.
John Wick's article talks about alignments reflecting Powers. So he makes a suggestion for use of a alignment subsystem and stuff. I'm not going to riff off that necessarily. Instead, here is my alt subsystem: Alignments as Icons (or at least heavily borrowing from the idea). Rather than track or maintain how much you stick to your alignment, this system instead helps generate some story based off what alignment you've put yourself in.
Like Wick's system, you get points to spend in Alignments. Unlike that system, these represent the Powers of Alignment, but players can only invoke them at dramatic times or they get rolled at the beginning of a session. For each point you have in a alignment, one d6 is rolled. On a 5, that alignment is involved and will help you overcome or find a solution to a situation. On a 6, the same happens, except there is a consequence to it.
Unlike with Icons, an alignment's influence in a situation is to provide solutions and help that fall within their purview. If Good is involved, that means you get help from someone doing Good or are presented with a chance to do something good, that also leads to you getting help or a clue of some kind. If Evil, instead someone kills or something dark that helps you- or you are given the chance to kill someone who'll have the critical information you need. And so forth.
The idea is to have the alignments steer some of the kinds of encounters that are going on. If players drift a bit darker, this system gives them encounters that reward that dark behavior. It also could reward a character for being lawful or chaotic or whatnot... Overall, its a tool to help define some plot or story elements based on player choice, like Icons do.
Also, like Alignment itself, you can retool this for any game outside of Pathfinder or D&D. Fate Core for example, could let you have this sort of subsystem or the traditional Alignment system. Of course, for Fate Core, each Alignment could be System-wide Aspects, invocable like any other aspect.
Lawful could be invoked to help create advantages tied to traditions or laws, or it could help reveal obscure traditions. It also could be compelled to cause a player to be inflexible on a issue, taking a conservative stance at a time where flexibility could be valued more. They surrender to the City Watch, being honest and obeying authority where others might choose to flee, for example.