IMHO, Mexicans simply do not see marijuana users the same way Americans do. For Americans, marijuana seems like a soft drug young people often try and later grow out of it. Sure, there is this argument about the gateway drug and all that, but at the end of day many conservative boomers did have first or second hand experience in the 1960's. So it's not a big deal.
Not so for the Mexican people. Specially in the urban population (which I suspect is overrepresented in the poll) the term "mariguano", describes not just a cannabis user, but a deviant user of any low cost drugs. It is low status, so it is easy to demonize, much like "crack-head" or "meth-head" in the US.
So, people is afraid of mariguanos. They do marginal jobs, if at all, then some end up resorting to petty crime to fund their habit. There is also a correlation between drug use and violent crime. I personally think that deviant types will display both higher use rates and higher violence rates than the general population, but most people assume causation right away.
It also does not help that the Catholic Church has taken a very clear cut stance about that. That is not the root cause of people feelings; if the Church took a similar stance against alcohol abuse, literally no one but a handful of old ladies would listen to them. But the Church (as a political agent) is scoring cheap points on the Supreme Court now, and there is very little cost to do that, so they keep doing it.
Therefore, the results of the poll reflect a feeling from the Mexican people: that the government is failing to protect them - again, - and betraying their interest - also again.
If the US does not legalize those drugs, then Mexico will have to take the cost of legalization without it's biggest benefit.
One big benefit of legalization of drugs was that the organized criminals wouldn't be able to make money off it, but most of their business is in the US anyway.
The crimes Mexican people most want to reduce are the violent crimes, the corruption, etc, all caused by people having to deal directly or indirectly with cartels if they want to produce/sell/consume drugs.
As long as the US keeps drugs illegal in their market, people will have to deal with the cartels to be able to sell there, and the US is the biggest market.
Maybe they understand that argument, but disagree with it.
I personally think it rather unlikely that legalization will lead to the dissolution of the cartels. In fact my first (paranoid, almost certainly wrong) thought was that the cartels had some sway with the Mexican Supreme Court.
Most of the time the people who disagree with you are not simply stupid or ignorant, but have different values and don't share all the same assumptions.
The 'war' in Mexico is mostly cartel vs cartel, not unaligned government vs cartel.
So what do they have to lose? That means possible more consumption and possibly less pressure from the non-corrupt portions of the government and/or less legal power for one cartel to wield against another. (They'll have to stick with charges for the rampant human trafficking and slavery by the cartels.)
The idea that the cartels will just dissolve away upon the emergence of legal marijuana and a subsequent Free Market Flowering of the marijuana industry just seems hopelessly naive. Yes, the mafia was, perhaps, not happy about de-Prohibition. But guess what: the American mafia and is still responsible for the majority of organized crime in its area of influence.  The legalization of alcohol did not stop the mafia. And the cartels are far more ingrained in Mexican society than the mafia ever was in America. Even assuming someone unaffiliated with a cartel starts growing and selling, and the cartels don't just kill him, they would certainly run protection rackets.
I did not consider this, i think that makes a lot of sense.