  Using next-to-leading order (NLO) perturbative QCD, we calculate the
diffractive contribution to inclusive dijet photoproduction in Pb-Pb
ultraperipheral collisions (UPCs) at the LHC and find that it does not exceed
$5-10$% in small-$x_A$ bins in the ATLAS kinematics at $\sqrt{s_{NN}}=5.02$
TeV. Its smallness is a result of the restricted kinematics ($p_{T1} > 20$ GeV
and $x_A > 0.001$), the large nuclear suppression of nuclear diffractive parton
distribution functions predicted in the leading twist model of nuclear
shadowing, and additional suppression due to QCD factorization breaking in
diffraction. At the same time, using looser $p_T$ cuts, e.g., $p_{T1} > 10$ GeV
and $p_{T i\neq 1} > 5-7$ GeV, we find that $(d\sigma_{\rm
diff}/dx_A)/(d\sigma_{\rm inc}/dx_A)$ can reach $10-20$% at $x \approx 5 \times
10^{-4}$. Also, applying our framework to proton-proton UPCs at
$\sqrt{s_{NN}}=13$ TeV, we find that the ratio of the diffractive and inclusive
cross sections of dijet photoproduction $(d\sigma_{\rm
diff}/dx_p)/(d\sigma_{\rm inc}/dx_p)$ is as large as $10-15$% for $x_p \sim 5
\times 10^{-4}$. An account of the contribution of Pomeron-Pomeron scattering,
which is not included in our analysis, should make this ratio somewhat larger.
