How to factor this conditional probability?

Bayes rule says that: $$p(mu,tau|y)=frac{p(y|mu,tau)p(mu,tau)}{p(y)}$$

which means $p(mu,tau|y)propto p(y|mu,tau)p(mu,tau)$, i.e. LHS is proportional to the RHS.

This is typically done in Bayesian analyses where you're interested in the form of the posterior distribution and get rid of the constant part that doesn't change wrt the RVs of interest. For example, a subsequent analysis might be interested in calculating MAP estimates for $mu,tau$ by maximizing the posterior, in which case $p(y)$ has no effect.