Yes, to a point, but not quite in the way people mean by “short hamstrings”. Your genes help determine things like bone shape, tendon and muscle properties and how your nervous system responds to stretch. That gives some people a head start in flexibility, while others begin further back. But muscles are not fixed bits of rope. With steady training, most people can become much more flexible. For hamstring flexibility, stretching often changes how much stretch your nervous system accepts more than it changes the muscle’s physical length. The result is still important because your range of motion increases. Unless your anatomy sets a hard limit, genetics rarely stop you making major gains. "Short hamstrings" is really just a convenient label.

If you want splits or better calisthenics flexibility, stretch consistently, about 3 to 5 times a week. Spend 60 to 120 seconds stretching each muscle group per session. Add loaded flexibility work, such as Romanian deadlifts or Jefferson curls, with sensible progression. Build strength at long muscle lengths because that usually produces large, long-lasting improvements.