Why does it matter?
The truth is, we should be focusing on our relationship with Christ.
Often we get sidetracked into doctrines and practices, but they can matter too.
For example, a Protestant invites a Catholic to a personal relationship with Jesus as Lord and Savior, so that the Catholic can be saved. But (in theory), the Catholic already has a personal relationship, and is saved (in a state of grace) and in fact is even more intimately related with Christ through the Sacraments, by which the Catholic is not just personally related with Christ, but receives Christ and becomes a member of the Body of Christ!
In this case, explaining the doctrines of the Sacraments, of salvation and grace, of the Body of Christ (the Real Presence and the Mystical Body, the Church) are all important to help the Protestant come to a fuller understanding, and perhaps enter into a deeper relationship with Christ himself.
Or perhaps the Protestant sees John 6 speaking of “feeding on the Flesh of the Son of Man” as hearing the word preached and reflecting on it in prayer. And in turn ridicules Catholics for our worship of an idolatrous “cracker.” Again, our doctrine of the Eucharist and the Real Presence may offer a truer understanding.
It matters for much the same reasons that these doctrines were developed in the first place–it’s not because we enjoy fighting and alienating people, but because the errors were leading people astray, and we needed the doctrines to end the fighting!