Should feature selection be part of an ML production pipeline?

It depends upon the situation. If the dataset and featurespace is small, it makes sense to deploy as not only that it is computationally viable, but the chances that feature selection outcome is very sensitive to the small data as the data changes. However, for large dataset, with very large feature space, the selected features are more likely to be the same, even on near future data updates. So not putting feature selection on production pipeline can be computationally frugal.