It's not common, and I can't say I've done it myself, but I know a handful of folks (maybe two?) who pursued both professionally. I know a handful of others who will casually stage manage things like workshops, readings, etc for smaller theatres, when the time commitment is relatively small.
With AEA as the union for both, there's an inherent risk of joining the union for one of those passions, while not ready to join for the other. I.e. if you join because you're ready to as an actor, you are then a member as a stage manager as well, and wouldn't be able to take non-union gigs (and vice versa).
There's also a risk of a theatre that you work with associating you with one of these jobs more than the other - so if they think of you as an actor, you're less likely to get hired as an SM there. Not to say that it's impossible to break that perception, but it's something to be prepared for.
As mentioned in the previous response, there's always a benefit in understanding the other roles we work with - it can be a real strength as a stage manager to understand the vocabulary, process, and needs of acting. I'm sure any future stage managers you work with while acting will also appreciate your understanding of what goes into their jobs as well!