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In a uniformly smooth and <i>p</i>-uniformly convex Banach space, let the pair of variational inequality and fixed-point problems (VIFPPs) consist of two variational inequality problems (VIPs) involving two uniformly continuous and pseudomonotone mappings and two fixed-point problems implicating two uniformly continuous and Bregman relatively asymptotically nonexpansive mappings. This article designs two parallel subgradient-like extragradient algorithms with an inertial effect for solving this pair of VIFPPs, where each algorithm consists of two parts which are of a mutually symmetric structure. With the help of suitable registrations, it is proven that the sequences generated by the suggested algorithms converge weakly and strongly to a solution of this pair of VIFPPs, respectively. Lastly, an illustrative instance is presented to verify the implementability and applicability of the suggested approaches.