Your two part question is really one. Shriners are Masons.
As to why Catholics are not allowed to join the Masonic Order, it is a simple case of irreconcilable differences. As (then) Cardinal Ratzinger pointed out in 1983: "[Masonic] principles have always been considered irreconcilable with the doctrine of the Church and therefore membership in them remains forbidden.
The differences relate to the general philosophy of the Masonic Order. They tend to be Deistic rather than the Catholic/Christian notion of God's presence and action in the world. They tend to be rationalists and do not generally accept faith as coequal with reason. Obviously there are regional differences and many people join them simply as a fraternal activity. But the Church sees the whole picture, not just individual pieces. On the whole, the guiding principles of Masonry are irreconcilable with the Catholic faith.