Rotating magnetized compact objects and their accretion discs can generate strong toroidal magnetic fields driving highly magnetized plasmas into relativistic jets. Of significant concern, however, has been that a strong toroidal field should be highly unstable to the non-axisymmetric helical kink (screw) $m=1$ mode leading to rapid disruption. We describe large-scale fully three-dimensional global general relativistic magnetohydrodynamic simulations of rapidly rotating, accreting black holes producing relativistic jets. Despite strong non-axisymmetric turbulence in the disc, the jet reaches Lorentz factors of $Γ≤sssim 10$ at distances of $10^3$ gravitational radii without significant disruption or dissipation with only mild substructure dominated by the $m=1$ mode. This implies astrophysical jets are roughly stable structures and may reach up to an external shock with strong magnetic fields. We study the accretion of small-scale and large-scale dipolar and quadrupolar fields, showing that only a dipolar field near the black hole allows a steady relativistic jet against disruption due to disc turbulence. We discuss the astrophysical implications of the accreted magnetic geometry playing such a significant role in relativistic jet formation, structure, and stability.