How do I avoid re-rendering a connected React PureComponent due to mapDispatchToProps functions?

I generally advise to not try to recreate functions that capture props values like that, but instead have a handler method on your class that passes prop values to the action creator. I also advise that people not write mapDispatch functions directly, but use the "object shorthand" for connect().

Example:

const actions = {addToStack : StackAction.addEpisodeToStack};

class MyComponent extends React.Component {
    addToStack = () => {
        this.props.addToStack(this.props.episodeId, this.props.stackId);
    }
}

In your specific snippet, it looks like you're not even referencing any props values in mapDispatch anyway, so there was no need to declare the ownProps parameter. (connect will only call a mapDispatch function multiple times if the ownProps parameter is requested. Otherwise, it only calls mapDispatch once, when the component is created.)