People(no matter the age) like to do what they're more comfortable with, and giving them things to do they don't like will only annoy them plus it can even make them hate the hobby. Plus if the hobby has nothing wrong then it doesn't matter if YOU don't like the hobby because is there life.
If a parent has the resources that would allow a particular hobby, then the child should be allowed to take up whatever hobby he or she wants to. In following his or her passion, the child may be led to a path in life for enjoyment or even for a career.
No, kids should not be allowed to take up any hobby they want to, because a parent should guide their child into a hobby that makes sense. A child's hobby needs to have training or supplies available in the area. A good hobby is also something practical that can be pursued for many years.