The principle objections against the Christian nature of Catholicism by a few Fundamentalist groups hinges on the belief of Sola Scriptura (Only Scripture) that was promulgated during the Reformation. Many of the practices and teachings of the RCC have developed throughout its 1900 years of existence (1400+ years at the time of the Reformation). In reaction to some of the very real abuses that had crept in to the practices, the reformers looked to find a single, solid core of belief that could not be corrupted by developing traditions. They turned to Scripture as that core.
That sounds simple enough, but life is never simple. Scripture did not appear in a void. It is the Catholic position that Scripture arose from Tradition and encapsulated the true core of the beliefs, but that Tradition does not die when Scripture is written and Tradition provides commentary and explanation on the Scriptures. Immediately, we are at an impasse.
Beyond that, there is the very question “What is Scripture?” For the Christian New Testament, all the Christian religions are pretty much in agreement. However, there were books in circulation at the time of Jesus that were looked upon as spiritual guides and were included by the early Christians as part of the Old Testament. After Christianity had gotten going, Jewish Scholars closed the Jewish canon, reviewing many of the works that the Christians were using and setting them outside the Jewish canon as not maintaining the actual beliefs of Judaism. 1400 years later, when Martin Luther was reviewing the whole Christian canon, he set aside any book that had not been included in the Jewish canon on the grounds that, if the OT is the Jewish testament, then we cannot include works that they do not include.
(It did not impede his decision, in any way, that several Catholic practices and teachings that he opposed were supported by appeals to those books.)
For the next 400+ years, Catholics and Protestants simply accused each other of abandoning the “real” Faith without much regard to what Christianity meant. In the 20th Century, the Ecumenical Movement looked on the Catholic/Protestant Schism as a scandal against the teachings of Jesus and many people have begun looking to see whether the groups have more in common than we originally fought about.
Some groups on each side, however, are much more comfortable damning their “opponents” than trying to come together in Christian charity. Among the Catholics, this is usually manifested by people claiming that Catholicism is the “One True Church” (often claiming that the Second Vatican Council was a hoax or worse). Many of these Catholic groups appeal to the memory of Pope Pius X as their patron while “defending” the church against heretical assaults. Among Protestants, this is usually manifested by people claiming that Catholicism is actually ancient paganism reborn,led by “the Whore of Rome” and all that gibberish.
(Catholics had a rallying cry for years, “Outside the church, no Salvation!” This has been understood for a good many years to mean that the whole Church (as the Body of Christ) including all the Christian community brings the message of Salvation to the world. Some Protestants (falsely) state that Catholics are still claiming that one has to be Catholic to be saved. In answer, I like to point out that the last Catholic priest in the U.S. who stood up and proclaimed that all non-Catholics were going to Hell was excommunicated for not backing down on that issue. [Fr.Feeney of Boston in the early 1950’s.])