Recent neural rendering techniques have greatly benefited image-based modeling and relighting tasks. They provide a continuous, compact, and parallelable representation by modeling the plenoptic function as multilayer perceptrons (MLPs). However, vanilla MLPs suffer from spectral biases on multidimensional datasets. Recent rescues based on isotropic Fourier features mapping mitigate the problem but still fall short of handling heterogeneity across different dimensions, causing imbalanced regression and visual artifacts such as excessive blurs. We present an anisotropic random Fourier features (RFF) mapping scheme to tackle spectral biases. We first analyze the influence of bandwidth from a different perspective: we show that the optimal bandwidth exhibits strong correlations with the frequency spectrum of the training data across various dimensions. We then introduce an anisotropic feature mapping scheme with multiple bandwidths to model the multidimensional signal characteristics. We further propose an efficient bandwidth searching scheme through iterative golden-section search that can significantly reduce the training overload from polynomial time to logarithm. Our anisotropic scheme directly applies to neural surface light-field rendering and image-based relighting. Comprehensive experiments show that our scheme can more faithfully model lighting conditions and object features as well as preserve fine texture details and smooth view transitions even when angular and spatial samples are highly imbalanced.