  [ABRIDGED] This paper discusses the importance of parallel perturbations of
the magnetic-field in gyrokinetic simulations of electromagnetic instabilities
and turbulence at mid-radius in the burning plasma phase of the conceptual
high-$\beta$, reactor-scale, tight-aspect-ratio tokamak STEP. Previous studies
have revealed the presence of unstable hybrid kinetic ballooning modes (hKBMs)
at binormal scales approaching the ion Larmor radius. In this STEP plasma it
was found that the hKBM requires the inclusion of parallel magnetic-field
perturbations to be linearly unstable. Here, the extent to which the inclusion
of fluctuations in the parallel magnetic-field can be relaxed is explored
through gyrokinetic simulations. In particular, the frequently used MHD
approximation (dropping $\delta \! B_{\parallel}$ and setting the $\nabla B$
drift frequency equal to the curvature drift frequency) is discussed and
simulations explore whether this approximation is useful for modelling STEP
plasmas. It is shown that the MHD approximation can reproduce some of the
linear properties of the full STEP gyrokinetic system, but is too stable at low
$k_y$ and nonlinear simulations using the MHD approximation result in very
different transport states. It is demonstrated that the MHD approximation is
challenged by the high $\beta^{\prime}$ values in STEP, and that the
approximation improves considerably at lower $\beta^{\prime}$. Furthermore, it
is shown that the sensitivity of STEP to $\delta \! B_{\parallel}$ fluctuations
is primarily because the plasma sits close to marginality and it is shown that
in slightly more strongly driven conditions the hKBM is unstable without
$\delta \! B_{\parallel}.$ Crucially, it is demonstrated that the state of
large transport typically predicted by local electromagnetic gyrokinetic
simulations of STEP plasmas is not solely due to $\delta \! B_{\parallel}$
physics.
