Conditional i.i.d.ness of random variables

Question

Let $X$ be a random variable with support $\mathcal{X}$. Let $r:\mathcal{X}\to\{0,1\}$.

Assume the random variables in the sequence $(\epsilon_i)_{i=1}^N$ are i.i.d. conditional on $X$.

Does this imply that the random variables in the sequence $(\epsilon_i)_{i=1}^N$ are i.i.d. conditional on $r(X)=1$?