Biases - practical application

Knowing that most of the individuals are biased, and assuming that those individuals are unaware of it - taking example of conservatism bias - does it mean that we shouldn’t update our beliefs as soon as new ‘complex’ info arrives because those individuals will take time to process and under react?

Context - markets can remain irrational longer than you can afford to be solvent; also assuming large number of market participants are biased and can move the market.