Inhomogeneous broadening is a major limitation for the application of quantum emitters in hexagonal boron nitride to integrated quantum photonics. Here we demonstrate that so-called blue emitters with an emission wavelength of 436 nm are less sensitive to electric fields than other quantum emitters in hexag-onal boron nitride. Our measurements reveal a weak, predominantly quadratic Stark effect that indicates a negligible transition dipole moment of the defect. Using these results, we discuss implications for the symmetry of the defect and use density-functional-theory simulations to identify a likely atomic structure of blue emitters in hexagonal boron nitride.