IMO the Pastorals advocate a middle way (cf. the constant appeal to sôphrosunè, "sensibleness", the middle-class ethical values, etc.) between Judeo-Christians and Christian Gnostics, and they fight on both fronts. Non-Christian Judaism and Paganism have already gone offstage.
This would put the Pastorals on similar ideological turf as the Ignatian epistles, which engaged in polemic against the same two groups. But did the author of the Pastorals really see any difference between Judeo-Christians and "Non-Christian Judaism"?