Is modernism, as defined by Pope Pius X in "Pascendi Dominici Gregis" (1907), still considered a heresy? If so, please discuss it in relation to the Church today.
The answer is yes. What Pope St Pius X defined as heresy is still heresy today, and his encyclical on the matter is well worth reading. But acknowledging this is a very different thing from agreeing with those on the Catholic right who declare this or that opinion or practice "modernist."
Let's give a simple definition of modernism: it is that ideology which reduces both divine revelation and the supernatural life of grace to being the result of a subjective attitude or tendency on the part of human nature. Modernism thus retains all the vocabulary and external forms of orthodox Church life but reinterprets them along the lines of modern, "subjectivist" philosophy.
There is not the slightest doubt that this heretical point of view affects the teaching of a number of modern theologians and that the results of their teaching are obvious in the Church today. Even so, there are significant modern theologians who were accused of modernism but who in fact were faithful Catholics and promoters of orthodoxy. Among them was Fr. Joseph Ratzinger! So we should be careful that when we disagree with a particular theologian (some reservations regarding Hans Urs von Balthazar come to mind) we should not be rash in imputing errors to them which in fact they rejected and fought against.
Modernism is a heresy, alive and well in many RCIA and diaconate programs, but it is rash and uncharitable to accuse anyone with whom we disagree of heresy. Some "progressive" opinions are in fact correct.