Simple answer: John Paul II had a problem with traditional Catholicism, not with Cardinal Kasper’s modernist ideas.
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Respect must everywhere be shown for the feelings of all those who are attached to the Latin liturgical tradition, by a wide and generous application of the directives already issued some time ago by the Apostolic See, for the use of the Roman Missal according to the typical edition of 1962.
Pope John-Paul II, Motu Proprio “Ecclesia Dei”
2 July 1988
John Paul II Oct 1998 address.
I invite the bishops also, fraternally, to understand and have a renewed pastoral attention for the faithful attached to the Old Rite.
There are to be classes in dogmatic theology which are always to be based upon the written word of God along with sacred tradition, in which the students may learn to penetrate ever more profoundly the mysteries of salvation, with St. Thomas as their teacher in a special way.
Code of Canon Law, 1366, 2
The people of God need to see priests and deacons behave in a way that is full of reverence and dignity, able to help them to penetrate invisible things, without unnecessary words or explanations. In the Roman Missal of St Pius V, as in several eastern liturgies, there are very beautiful prayers, through which the priest expresses the deepest sense of humility and reverence before the Sacred Mysteries : … they reveal the very substance of the liturgy.
Pope John-Paul II, Address to the Congregation for Divine Worship
Castelgandolfo, 21 September 2001