There's no penalty just for rejecting a duty once, and generally you can commence the duty without leaving the cutscene or skipping it as long as you are currently the correct job.

That said, some cutscenes don't let you do that, and it's frustrating if you've been sitting in a queue for a while and your choice is to skip the cutscene to accept it or face the long wait over again.

Generally I work around it by trying not to get into cutscenes while queuing for stuff, and do other activities like minor sidequests or sorting out retainers and glamours.