BBQ or cooking on a charcoal grill using charcoal has the potential to produce cancer causing compounds.
However I would not worry about it.
Thousands of people cook on the BBQ grill with charcoal and have done so for many years now and haven't gotten cancer.
I sometimes cook on charcoal grills when at campsites and I like the taste of the food from it.
I don't worry about it myself and if it were not really safe then charcoal would not be allowed to be sold.
You can get cancer from many other things and cooking with charcoal you have a low chance of getting cancer or other health issues.
If you're worried then you can use regular dried out wood to cook food with on a charcoal grill.