The Monte Carlo simulation method in the grand canonical ensemble has been used to study the wetting behavior of highly non-additive symmetric mixtures in contact with selective walls. We have focused on the behavior of the mixtures, which exhibit closed immiscibility loops in the bulk, and have investigated the interplay between the surface selectivity and the wetting properties of the adsorbed mixtures. Different wetting behaviors has been found, depending on the values of the adsorption energies of the mixture components. We have considered the systems in which the wetting at non-selective walls occurs at the temperatures below the onset of the demixing transition in the bulk. When the average value of adsorption energies is fixed, the wetting temperature has been found to be unaffected by the weak selectivity of the wall. In this case, the reentrant mixing has been observed in thick adsorbed films. However, when the wall selectivity increases beyond a certain threshold value, the reentrant mixing in the film has been suppressed. This leads to the increase of the wetting temperature. In the case, when the adsorption energy of one component is fixed, while the adsorption energy of the second component changes, the wetting temperature has been found to exhibit non-monotonous changes with the difference between the adsorption energies of the mixture components.