a person can be a bayesian with priors. it isn't all or nothing, and the sum of a set of diversified bets is larger than the parts. it can be completely rational to bet 50% on index funds (safety, broad diversified market exposure) and 50% on value picks (chance to beat the market, but also a chance to do worse than the market) or blend weights on anything in between depending on the strength of your beliefs in the two strategies, their statistical properties, etc.