Kinetics of localized adsorption of interacting spheroidal particles on homogeneous interfaces was analyzed theoretically. In contrast to previous studies, in our present approach an unoriented (quasi-3D) adsorption of prolate and oblate spheroids was considered. By applying the random sequential adsorption (RSA) method, numerical Monte Carlo type simulations were performed for colloidal particles interacting via a repulsive potential stemming from the electrostatic double-layers (exponentially decaying Yukawa-type potential). The surface blocking parameter (available surface function) and adsorption kinetics were determined for various particle shapes and for a broad range of the Ka parameter characterizing the range of the interaction potential. It was demonstrated that the "exact" numerical results can well be described for not too high surface concentrations by the approximate analytical expressions derived using the equivalent hard particle concept. On the other hand, for surface concentrations close to jamming, adsorption kinetics of interacting particles can well be approximated by the power-law dependencies analogous to hard particles. The theoretical analysis revealed that adsorption rate of colloid particles having a spheroidal shape is considerably diminished by the lateral electrostatic interactions.