I'd like to add my own observations. The police are paid very low wages, barely livable -- under their uniforms in the some cases is the most threadbare underwear -- if they are not proficient yet, or they are honest -- in collecting "user fees".
The response time to an emergency call runs very long -- 45 minutes at minumum, and longer if any response at all. I saw this on some investigative TV show when I was there, as well as anecdotal reports from local co-workers.
The Law, courts, etc. is all by connections, well-established family connections. Not connected? No luck for you.
(Side note: Don't buy property in Mexico -- the deeds of us gringos are just about worthless, they'll figure out some way the land doesn't belong to you, and all you'll have to show for it is your lawyer bills.)
In a way, the law is open -- to persons of energy and vigor and money to spread around. You don't see people hanging around at crosswalks three minutes for a WALK signal on an empty street like you will in Germany and Switzerland. People do what they will to get where they want to go -- on the sidewalk and street and in business and the courts. The rules are "flexible". Yet there is a snide pride in some, and in such a situtation you may not be able to go on directly but must seek agents and intermediataries to get around things.
Bribes and kickbacks are common -- a gringo I know of almost lost his job because his workers didn't trust him -- he wouldn't take the payday kickbacks that were the norm. In a way they felt dishonored.
Religiously, Mexico is an unstable mix. Every calendar will have the Saints Feast Days on it -- that is every single day has it's saint. Veneration of statues of Mary is common. You'll have the most despicable, disgusting place and right in it and well-kept beautiful statue with fresh flowers. Yet the state has a history of hating and actually warring against the church clerics.
Mexico had it's godless secular state long before the godless Marxists detrained in Russia.
There are three great things that make Mexico's law and policing systems so rotten, imo -- rotten in our eyes, that is. They are as you may be suggesting, the strong scent of that deadening form of religious worship known as idol wqorship, preserved not only from recast ancient native practises, but also from the idolatrous Chritianity of many of the conquisadors and clerics. One aspect of that idolatry -- to my view -- is the hard anti-religiousity of the secular state.
The second is the massive mess of the Spanish Codex they inherited, that even in Spain at the time of the colonization of Mexico engendered a grave disrespect for the laws, as an overabundance of laws causes abitrary, haphazard enforcement. The refuge was in family circles, the rule of by a basically non-tyrannical, yet self-serving, small group of elite families, who kept judges and officers in their extended household.
The third is the lack of respect for the laws of agency and contracts by agents. It was a deep and active regard for laws of agency and agents that empowered English colonial experience. Without resepct for the independent actions of agency and agents, micro-management is prevalant, stumbling blocks are set at every distant turn.
The second is the massive mess of the Spanish Codex they inherited, that even in Spain at the time of the colonization of Mexico engendered a grave disrespect for the laws, as an overabundance of laws causes abitrary, haphazard enforcement.
And,
The Law, courts, etc. is all by connections, well-established family connections. Not connected? No luck for you.
And further;
micro-management is prevalant, stumbling blocks are set at every distant turn.
I'm thinking of Kafka's "The Castle"