I was hesitant to post in this thread. But - maybe it'll help, hope it doesn't hurt.
Mexico, like the US is a land of differences. It's hard if not impossible to judge the whole country, as there are good and not so good, and downright bad parts. Anyone seeing Orlando, and then going to downtown Detroit would be amazed it's the same country.
I grew up in SoCal, and was going in and out of the Mexico around the border towns since I was a kid with the parents. The border towns are resilient, and the most liberal culturally because of the US influence. Once you get past the border towns, the interior of Mexico has a lot of different faces, and significant cultural themes. My GF who went with me to Cancun, and down the Yucatan was kind of surprised to find native Mexican 'indians' or indigenous people who rarely see white folk. Then, there are the Castillian/Spaniard breed from the central mountain areas, and all the Mestizas in between.
Some states are better to stay out of, like for me it was Vera Cruz. Quite a bit of unrest there for many years. Tamaulipas is another one that's best left alone, as is Oaxaca unless you are moving fast, or obviously a poor Norte slumming along. Pretty much anywhere there is a lot of travelers you are going to be ok. Border areas, The Yucatan, most large cities like DF and of course the coastal tourist areas. They rely on tourist income, so there's rarely a problem.
I stopped going to Mexico about 10 years ago. It's gotten worse for US citizens, and without pointing too much fault not all of it is due to their culture. There are thriving ex-pat communities, the best known is near lake Chapala. I think that most US citizens that wind up getting in trouble in Mexico were prolly looking at some kind of trouble anywhere, including the US.
Sadly, there is a thriving and I think growing economy in kidnapping for ransom. This case isn't going to make things better, and likely will make it worse. The family paid up, and the victims were killed, and no one has been caught giving rise to a successful action all the way around for the kidnappers. I used to drive ratty cars into Mexico, and would never drive a real nice car there. Nor would I go if I were wealthy unless I had a well trusted security detail, including guns, which is very hard to do in Mexico.
Crime stats generally favor the US over Mexico, particularly for violent crimes. However, there is a caveat that many of the violent crimes in Mexico are between drug dealers, and their protection details. I'm pretty sure if you stay in major cities, or areas where there are a lot of US people, crime potential is very low, and crimes in tourist areas are usually solved, and offenders punished to promote safe tourism.
It's a beautiful place. They have a huge grand canyon of their own, beaches, reefs, thriving night life, but they are still a 3rd world country with all that entails.