From what I have seen, when most Bishops and the Pope meets with and prays at a Non-Catholic Church, Temple or Synagogue, they are going there to put forth the hand of Christian love and compassion as well as being official representatives of the True Faith, reaching out to those who may not know the full love of Christ. When they pray, either in private or with other leaders, it is not to any False gods, but to the True God, and I would imagine it is for true dialogue. They do not receive communion, or normally participate in the Worship of those groups. The only exception I know of (for a Pope) is Pope Paul VI attended a Greek Orthodox Liturgy but he did not activly participate.
As for casual attendance at Protestant or other services we do not officially represent the Church, and would not be attending a Worship service as such. We can pray for Christian unity with Protestants, but not as part of Protestant worship. We can attend Weddings and funerals as well as other functions like a bar-mitzvah, but not participate in an active manner. We do this out of respect for family or friensd. (unless it is a Catholic who abandons their faith to marry in another religious or civil ceremony.)
There are some bishops who have been accused of going too far, but they deserve two things. First our Prayers, as their job is very difficult, and secondly the judgement of the Pope, and not ourselves. While we can express our concerns to the Vatican, we really are in no position of authority to judge these bishops.