Dominican Republic is a destination with lots of all-inclusive hotels. Most of the guests stay in the hotels (you'll find many Europeans as it is one of the cheapest Caribbean destinations for us). This means people there have a low chance to earn money from tourists (as the hotels are owned by foreign companies).

So , in the environment of the hotels there sure are people who try to cheat you (To my opinion tourists should accept to be cheated if it's not too bad ).

But I never have heard of systematic date raping or something.. Of course a young female person in a Latin country should always be careful and it would not be recommended to visit a bar alone and drink etc. as this will be misinterpreted. But this is true for most of the places where you travel alone.

Try to buy a good travel guide and read the warnings of the state department too.