I've been to that area, and would consider it safe during the daytime. Like many areas of the world, it sounds like the night has its own cast of characters. I can see the potential for danger at night. The people are very poor, and there will always be a segment of the population who are driven by their addictions or desperation.
Belize is an interesting place. The majority of the population are descendants of slaves, unlike the Hispanic countries around them. They are very young, because of their history. Some time ago, the majority of working age people left the country in desperation, planning to send money back when they found work. The children were left in the care of their grandparents, who have since passed away, and the parents never came back. The remaining generation has a strong Christian base, instilled in them by their grandparents. Love for their fellow human beings seems to be important to them, and the people will often offer a kind word or directions to tourists.
Out of the city, nearly every shanty is a business of some sort, selling everything from fruit to medical services.
Most homes are built on stilts because of flooding in the rain forest-like setting. The major archaeological sights are cared for by small colonies of people. They are happy to talk, even if it is clear you are not purchasing anything.
In many ways, Belize is like Jamaica. The people live day to day, smoking their worries away. It is paradise and poverty, all wrapped up in one.