  The Event Horizon Telescope, a global submillimeter wavelength very long
baseline interferometry array, produced the first image of supermassive black
hole M87* showing a ring of diameter $\theta_d= 42\pm 3\,\mu$as, inferred a
black hole mass of $M=(6.5 \pm 0.7) \times 10^9 M_\odot $ and allowed us to
investigate the nature of strong-field gravity. The observed image is
consistent with the shadow of a Kerr black hole, which according to the Kerr
hypothesis describes the background spacetimes of all astrophysical black
holes. The hypothesis, a strong-field prediction of general relativity, may be
violated in the modified theories of gravity that admit non-Kerr black holes.
Here, we use the black hole shadow to investigate the constraints when rotating
regular black holes (non-Kerr) can be considered as astrophysical black hole
candidates, paying attention to three leading regular black hole models with
additional parameters $g$ related to nonlinear electrodynamics charge. Our
interesting results based on the systematic bias analysis are that rotating
regular black holes shadows may or may not capture Kerr black hole shadows,
depending on the values of the parameter $g$. Indeed, the shadows of Bardeen
black holes ($g\lesssim 0.26 M$), Hayward black holes ($g\lesssim 0.65 M$), and
non-singular black holes ($g\lesssim 0.25 M$) are indistinguishable from Kerr
black hole shadows within the current observational uncertainties, and thereby
they can be strong viable candidates for the astrophysical black holes. Whereas
Bardeen black holes ( $g\leq 0.30182M$), Hayward black holes ($g\leq
0.73627M$), and non-singular black holes ($g\leq 0.30461M$), within the
$1\sigma$ region for $\theta_d= 39\, \mu$as, are consistent with the observed
angular diameter of M87*.
