I saw that same website. It is maintained and posted to by Catholics who subscribe to the idea that the Catholic Church has been divided since Vatican II, and that every Pope since then has, to a greater or lesser degree, been counter to what they believe to be the “True Catholic Church.” They are sometimes referred to as ‘Pius XII Catholics.’
Receiving the Eucharist in the hand, conducting a Mass in other than Latin, encouraging any other religious practice (ecumenism) than pre-Vat II Catholicism, and certain traditional things such as women wearing Mantias in Church, etc.
What has been high on their list of anti-Catholic, anti-Pope activities is all activities that take place under the label of ecumenism. The feelings they seem to have about the ecumenical movement is that it diminishes what the Catholic Church stands for - ie praying at the wailing wall as both Benedict XVI and John Paul II did. It’s all a sell-out by our Holy Father(s) and leads all Catholics down the path to perdition.
There is also another group who call themselves ‘American Catholic Church’ who subscribe to beliefs like women priests, pro-choice, etc. They call themselves Catholic and consider themselves loyal to the Papal office, even though they have these beliefs that don’t submit to Papal authority. We used to call them ‘cafeteria Catholics’ - a little of this and a little of that.
I can understand your concerns when you encounter these beliefs under the name of Catholicism. That is a flaw in the Internet. I even once found a website that was set up by a ‘Pope Philip’ in Cleveland who claimed to be the legitimate descendent of the Papal authority from Vatican II. I don’t believe that Pope Phil from Cleveland is out there anymore, either having died or been committed.
Pray always for discernment, and never trust one website or one book to be true. Always look for your own corroborating information or rely on Catholic Answers.