  We consider the expectation value $\langle \cal W \rangle$ of the circular
BPS Wilson loop in ${\cal N}=2$ superconformal $SU(N)$ gauge theory containing
a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and
antisymmetric representations. This model admits a regular large $N$ expansion,
is planar-equivalent to ${\cal N}=4$ SYM theory and is expected to be dual to a
certain orbifold/orientifold projection of AdS$_5\times S^5$ superstring
theory. On the string theory side $\langle\cal W \rangle $ is represented by
the path integral expanded near the same AdS$_2$ minimal surface as in the
maximally supersymmetric case. Following the string theory argument in
arXiv:2007.08512, we suggest that as in the ${\cal N}=4$ SYM case and in the
${\cal N}=2$ $SU(N) \times SU(N)$ superconformal quiver theory discussed in
arXiv:2102.07696, the coefficient of the leading non-planar $1/N^2$ correction
in $\langle\cal W \rangle $ should have the universal $\lambda^{3/2}$ scaling
at large 't Hooft coupling. We confirm this prediction by starting with the
localization matrix model representation for $\langle\cal W \rangle $. We
complement the analytic derivation of the $\lambda^{3/2}$ scaling by a
numerical high-precision resummation and extrapolation of the weak-coupling
expansion using conformal mapping improved Pad\'e analysis.
