The "Protestantizing" tendency you note in some Catholic circles is not necessarily causally connected to the relatively recent influx of Protestant converts to the Church. On the contrary, many converts enter the Church looking for a much more traditional liturgical worship and strong adherence to Church authority and discipline, and are disappointed to find practices and patterns that very much resemble what they had hoped to leave behind in Protestantism.
Liturgical abuses are often either spontaneous innovations or are introduced by hopefully sincere but misinformed liturgists. In either case, the way to address the innovations is the same: Give your pastor the documentation that proves that these innovations are not in line with the Church’s liturgical guidelines and request that, based on this documentation, he end them.
As for the remark by the Catholic convert that "cradle Catholics" are not true Catholics, obviously this is an unjust generalization. The sacraments are what make us true Catholics, not how well we use the graces the sacraments give us. If some cradle and convert Catholics refuse to live up to the requirements of the faith, they are still Catholics, though poor ones.