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I also have a bachelors in psychology, and I've been fortunate enough to have landed a job that I love, supervising/managing several different mental health programs. Although degrees can open doors and create opportunities for you, it isn't the only qualifier in getting opportunities for jobs. Depending on what you like to do (working w/ teens, elders, managing funds, setting up fundraisers, etc.), there will be opportunities for you. Psychology is a versatile degree, and should allow several doors to open for you.
You'll need to look at what you would like to do in your future (5 year and 10 year goals). Psychology is definitely a great degree to have when working with non-profits.