A significant fraction of new mutations confer no immediate selective advantage to their bearer. Far from being irrelevant to evolution, the accumulation of neutral variation can pave the way for the discovery of fitter phenotypes and their subsequent positive selection, thus linking robustness and evolvability at the molecular scale. Here I show that the interference of multiple neutral mutants in large populations puts sharp constraints on the navigability of neutral networks, in effect shutting off access to neutral ridges and inducing localization in dense cores within these networks. These results imply that neutral evolution may not allow for the continuous generation of new genetic variation, even when the underlying neutral network percolates through sequence space; in some cases, the likelihood to evolve a particular genotype can decrease with the population size. I illustrate these counterintuitive effects and their implications for evolvability by revisiting two classical examples: Maynard Smith's word-game model of protein evolution, and the structural network of a short RNA. Interestingly, the phenomenon of neutral interference connects evolutionary dynamics to a Markov process known in network science as the maximal-entropy random walk. From this connection follows a new optimization principle in evolution: in the strong mutation regime, neutral evolution chooses those mutations which increase the Shannon information of substitutions at the highest possible rate.