Yes, basically Mexico is safe. The violence is mostly between members of the drug cartels.
I don't know where you live, but I live outside of Philadelphia and there are shootings there every day. Does that mean the US is not safe?
We have never felt unsafe in the area you intend to visit.
Just use the same common sense you would use anywhere else and you will be fine.

We have just returned from seven weeks travelling around various parts of a Mexico and felt as safe, if not safer, than anywhere else we have travelled in the world.

I vacation (solo/female) twice a year on "the other side" in Puerto Vallarta...

But from what I have read, any recent violence in that area you are asking about was not against tourists. While disconcerting, the murders are Mexican to Mexican. and most often cartel business nothing to do with tourists and normally no incidents in tourist areas.

My wife and I have lived in Mexico full time for some 9 years now and travel the country extensively. While there are places to avoid, Riviera Maya (just returned from Isla Mujeres) isn't one of them. Violent crime and assaults against tourists are extremely rare. Petty crime such as pickpocketing, overcharging by taxi drivers and vendors is probably the worst you might experience. That and an occasional police shakedown if you rent a car. Safety standards having to do with building and electrical codes and such however can be lax compared to the US and Canada. So some care is needed when you're out walking around after a few drinks.

I don't believe that Mexico is entirely safe, however, I didn't feel unsafe at any time during my vacation and my daughter/friends have been couple of times without incident. And I would go again without hesitation, but next time I will be more aware about crime in Cancun than I was before, not that it changes anything. Crime is not usually against tourists but it does occur in tourist areas and tourists could be caught up in it. I don't understand why violence between locals but not against tourists makes a place more acceptable but that's how it is. You might find this programme which was aired on UK TV couple of years ago, interesting, it can be seen on Youtube, called Unreported World, Mexico Beach Wars.

I don't understand why violence between locals but not against tourists makes a place more acceptable but that's how it is.

I don't think it "makes a place more acceptable" at all. At least that's not how I would say it. Rather that statistically it is unlikely Mexican-among-Mexican affairs will affect you as a visitor.

I do not believe all of Mexico is entirely safe, that would be impossible in any country.

When talking about visiting a place, risks to visitors are important considerations. It's not that other things going on in the country aren't important. They just aren't a risk to visitors.

China's treatment of Chinese Muslims is absolutely horrible, and this concerns me greatly. However, when I traveled to China last year, as a non-Muslim visitor, this situation had no affect on me personally, so it wasn't one of my travel concerns. It's the same with most violence in Mexico - the situation with Cartel violence, corruption, etc is terrible - but it is very unlikely to affect visitors.

We've been going to various towns on the Riviera Maya for over 10 years - never felt any kind of danger. The locals are extremely friendly. There are tens of thousands of visitors from all over the world enjoying this beautiful area every day.

If you keep your wits about you and don't go off buying drugs or walking around in bad neighbourhoods, you will be fine.

I've felt very safe in the coastal regions

If it is true that lately. the wave of crime has greatly affected Mexican tourism, however a tourist should not worry so much, since most of the deaths are between members of the different cartels, a very clear example is the destination of Cancun, it is going through a very bad time however, if you are a tourist and you spend it in the safe areas (hotel zone of Cancun) you will not have to take any risk.