Including Collider Variables in Prediction When the goal is to estimate a causal association between X and Y in the regression framework, one should not condition on (include as covariates) collider variables (common causes of both X and Y) since doing so may introduce spurious/non-causal associations that bias the coefficient estimate for X (Berkson's paradox). 
My question: can including collider variables as potential predictors in a classification/machine learning framework also cause problems when accurate, generalizable, and useable prediction of Y is the goal? I.e. does the causal problem also lead to a prediction problem?
 A: No, causal problems do not lead to prediction problems. In fact, in your case, the "problem" may actually allow us to improve our prediction!
Suppose the graph is simply $X \rightarrow C \leftarrow Y$. Then $X$ and $Y$ are d-separated, which means that they will be completely independent. Also, the effect of $X$ on $Y$ is identified without the need to condition on further variables. Estimation will show that $E[Y|do(X = x)] = E[Y|X = x] = E[Y]$. THis also means that $X$ alone is not useful to predict $Y$. 
However, if we do not care about the causal effect, but merely want to predict $Y$, we will find that
$E[Y|X = x, C = c] \neq E[Y]$
because conditioning on the collider $C$ opens up a path between $X$ and $Y$. This will mean that a reliable variable selection procedure should pick up both $X$ and $C$ as relevant predictors. At the same time, conditioning on $C$ is invalid for causal inference.   
One comment on wording: $E[Y|do(X = x)]$ is the mean of $Y$ if you set $X = x$ externally. Estimation of this quantity from data allows you to predict what happens when you $do(X = x)$. $E[Y|X = x]$ allows prediction of $Y$ when you see $X = x$. Both tasks may be useful, depending on the context. 
