A few restrictions
In general, people with diabetes can - and do - take part in most sports and activities.
There are, however, some sports governing bodies that restrict involvement from people with certain medical conditions, including diabetes.
For example, people whose diabetes is treated with insulin or sulphonylureas are not usually allowed to pilot a plane or do a lone parachute jump (tandem parachute jumps are usually allowed).
Certain sports like scuba diving may have strict guidelines, but this is for your safety as much as anything else.
Get in contact with the sporting body (via the internet is a good way) or your local sports group to find out more.