Consensus networks are widely deployed in numerous civil and industrial applications. However, the process of reaching a common consensus among nodes can unintentionally reveal the network's topology to external observers by appropriate inference techniques. This paper investigates a feedback-based resistant inference design to prevent the topology from being inferred using data, while preserving the original consensus convergence. First, we characterize the conditions to preserve the original consensus, and introduce the "accurate inference" notion, which accounts for both the uniqueness of the solution to topology inference (solvability) and the deviation from the original topology (accuracy). Then, we employ invariant subspace analysis to characterize the solvability. Even when unique inference remains possible, we provide necessary and sufficient conditions for the feedback design to induce inaccurate inference, and give a Laplacian structure based distributed design. Simulations validate the effectiveness of the method.