There are no areas to avoid as such, but be careful to go to the residential neighborhoods at night. These neighborhoods can be quite deserted when it is dark and, since the area is still very developed, most of them lack public lighting. To completely avoid any possible taxi safety issues in Tulum, try to always take taxis in groups of 2 or more. I took a lot of taxi alone and I never had any problems, but to eliminate any possibility or anything bad that happened, staying in groups is a good idea.
It is best to plan your trip to Tulum during the low season, which means avoiding the end of December, February to April and the peak summer season. Look for white cars with the red stripe on the side, take note of the license plate before climbing and avoid travelling alone at night. Most crimes in Tulum are drug-related, so if you avoid putting yourself in situations like this, you should generally be fine. Basic things like avoiding unlit areas at night, renting your own car, and not accepting drinks from strangers are vital to ensuring you have a positive and safe experience in the city.
While there are some things you should avoid and other things you shouldn't do in terms of food safety, there isn't much stopping you from eating tacos or eating burritos. While swimming at midnight after bars seems like a good idea, if you've been drinking, avoid the water and try to stay consistent to get home in one piece. Alcoholic drinks in Tulum are something that happens, but it is completely avoidable as long as you don't get completely drunk and take care of what you consume. Thus, you will spend your holidays having everything in the hotel and, therefore, you will avoid being in the wrong place at the wrong time.
Taxis are almost inevitable if you want to explore Tulum, so it's good that they are as practical, well-regulated and as safe as they are. When it comes to areas you should avoid in Tulum, you should be careful not to wander around residential neighborhoods at night, as there is a lack of street lighting, which makes it easy for someone to sneak up on you. Misdemeanors are a problem in Mexico, so it's best to avoid using flashy items when traveling, just to avoid unwanted attention.