You're only limiting yourself if you allow yourself to be limited. (That sounded more Yoda-esque than I meant it to)
What I mean is, if you go to a liberal arts school for your undergrad theatre degree, you will have PLENTY of opportunity to take classes outside of your theatre major. In fact, these classes (like psychology, sociology, writing, math, economics, biology, anthropology, etc.) will be required by many schools for you to graduate. Many theatre majors have a minor in something like Poli-Sci, economics, sociology/psychology or writing as it helps them have interests (and a life!) outside the theatre department.
If you go to a school with a conservatory theatre program you may be more limited in terms of what classes you will be taking.
Keep in mind that the skills you learn as a stage manager and theatre practitioner are still valuable skills to have for jobs outside the theatre world. If you want to apply for a non-theatre job to expand your horizons, ask a non-theatre friend/parent to look over your theatre resume (or just tell them about your skills) and they can help you "translate" your theatre experience into words that non-theatre employers will understand and value.
I graduated from college with a BA in Drama and never thought for an instant that I was pigeon-holing myself or putting myself in a corner with my degree. I learned a great deal about theatre in school, of course, but I also learned a great deal about life, people and the world during my college career. It may sound hokey and old-fashioned, but it's true. There are also many stage managers that didn't go to college or went to college for something else entirely; Don't allow your degree to limit you or own you. Make the best choices for you with whatever degree you decide to pursue.