Fr. Hugh, you said, "It is true that some religions come very close to basic natural truths about the nature of God." Why is that? Why do some other pagan religions resemble Catholicism? It's very scary.
Take a look at the first chapter of the epistle to the Romans, and there you will see how St. Paul depicts the basic religious knowledge of the pagans. Take a look also at his sermon in Acts 17 to the men of Athens. All religions resemble each other in various ways, because the are the religions of human beings. The idea that the true religion should look or feel totally different from false ones is unfounded and dangerous.
St. Justin Martyr in his Apology points out that the mythology of the Greeks and the revelation of the Bible can be shown to be similar insofar as God or the gods intervene in visible, human life, and in human form. The fact that we all have a liturgy and images and various rites to mark the events of life from birth to death only indicates that we are dealing in religion with the realities of the life of men and women on this Earth. The visuals are not the most telling part, rather, that is what we believe about God and the world to come that is of importance, and what we believe about how we can obtain eternal life, following the means given us by our Savior.
Yes, all religions have washings, and sacred meals, but all do not make the same claims or have the same meaning as the religion established by Jesus Christ. So do not be scared that there are these similarities, but rather think it normal that these similarities exist, because God the Son chose to live and die as a human being. His revelation is accessible to everyone, and therefore has resonances with the experiences of everyone.