I do have a few thoughts here.

First, I’d generally suggest not doing data lookups directly in render functions. That should be handled in your mapState functions.

Second, the lookups and filtering should really be handled in memoized selectors, both for encapsulation and to improve performance.

Third, while storing the entire list of item IDs may not always have a particular benefit, storing lists of IDs is a key way to indicate some filtered or ordered subset of the items. See Dan Cousineau’s post Advanced Redux Entity Normalization for examples.