Can air be regarded as a constraint body when a rigid body is moving? Or is the moving itself cause the friction so it is an active force?
I do not think the terminology "active Force" and " forces of constraint" carry different meanings- one can ask: Are there any inactive Forces? If a force becomes inactive its effect will not/should not be there on the motion .
By inactive force if you mean "adjustable forces" like force of static friction - then its also "active" when it adjusts its value and prevents the relative motion with respect to the surfaces in Contact.
The air resistance on moving bodies are a type of constraining force but its non -holonomic in character as it can not be expressed as a constraining equation of the type f(x,y,z ) =0 ;
Its constraining equation will involve time and velocity of the body explicitly.
If a body is say falling in air -the layers of air in contact with the body will exert a frictional force opposing the motion which can be proportional to velocity or some power of the velocity and acts opposite to the direction of motion .So its active as well as constraining