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We introduce a variant of the voter model in which agents may have different degrees of confidence on their opinions. Those with low confidence are normal voters whose state can change upon a single contact with a different neighboring opinion. However, confidence increases with opinion reinforcement and, above a certain threshold, these agents become zealots that do not change opinion. We show that both strategies, normal voters and zealots, may coexist, leading to a competition between two different kinetic mechanisms: curvature-driven growth and interfacial noise. The kinetically constrained zealots are formed well inside the clusters, away from the different opinions at the surfaces that help keep the confidence not so high. Normal voters concentrate in a region around the interfaces and their number, that is related with the distance between the surface and the zealotry bulk, depends on the rate the confidence changes. Despite this interface being rough and fragmented, typical of the voter model, the presence of zealots in the bulk of these domains, induces a curvature-driven dynamics, similar to the low temperature coarsening behavior of the non-conserved Ising model after a temperature quench.