How common is it for academics to write fiction?
I am an academic and a professional writer. In my particular field of writing (interactive fiction), a large chunk of writers are academics, so it’s definitelt possible. 

Most employers are not concerned about outside activities as long as they don’t interfere with your responsibilities. However, writing commercially requires a large enough time commitment that it will be very hard to conduct research at the same time. The most prolific and successful academic/writers I’ve seen either stopped writing or stopped being a research academic. A few are able to find a position where there writing is valued as academic research (such as Nick Montfort). 

If research is an expectation for your position, then your best bet would be to take a more teaching-focused job or to work only a small amount of time each day and marketing your writing after you finish it in your own.